
Source:David Eppstein/Wikipedia
Irvine, Chicago and New York huh? Sounds very cool. Will definitely come up with ideas for you to find your groove in these places. All three are quite different cities so will try and satisfy all your requirements.
IRVINE
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Experience the Dinner Detective Murder Mystery Dinner Show - Don't expect too much from the food and I think you might come home satisfied with the experience of doing something unusual. Located inside the Atrium Hotel, this interactive murder mystery dinner show provides the ultimate entertainment experience. Their website lists 10 reasons why this is a MUST DO but note that $69, it doesn't come cheap.
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Give a free rein to your sweet tooth at SweetSpot Baker's Workshop. Choose your gourmet, fresh-baked cupcake flavor, choose your frosting and get all the toppings you want from their Wall of Sweets. Then make your cupcake the way you like it. Sounds like fun I bet
Do see this Yelp review for more.
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Drive for a hour from Irvine to Temecula and do the whole sniff, taste and spit routine at any of these wineries. There's an event happening on 22nd where proceeds are going to the local schools. Might be a fun thing to do.
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Check out various Indian dance traditions at the Barclay Theatre on May 23 called Nachle India 2. Tickets range from $18-$38.
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Check out the Chinese at Sam Woo's in Irvine. Have a read on Tripadvisor for a mixed bag of reviews.
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Get the giggles with a comedy night at the Improv. Again the food is good but the laughs might make it worth it. Jay Mohr is on May 22nd and 23rd. Have a look here for more information.
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For something silly yet fun, you want to consider taking the train ride at the Irvine Regional Park. Check here for more information.
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As a last, why don't you try Fresh fruit + Gelato + Shaved Ice at Mochilato in Irvine? Check out the fruitilicous photos here to make up your mind.
I thought I would leave you with one last tidbit about Irvine: Sudhir Alladi Venkatesh, sociologist and urban ethnographer is a native of Irvine. Now of course the chances of you bumping into him are very less but I thought this could be a fun fact for you! 
CHICAGO

Source:Peterfitzgerald/Wikipedia
Come and show me another city with lifted head singing
so proud to be alive and coarse and strong and cunning
Chicago - Carl Sandburg
Chicago - skyscrapers, blues, gangsters, comedy, where white collar rubs shoulders with blue collar, where there is true blue Midwestern friendliness. The best way to see Chicago is through the subways and elevated tracks. I will be recommending some stuff for The Windy City for you. Hope you find this information useful.
TIP: The best ways to get around Chicago are by El train, by bus and by foot, reserving cabs for late nights or lazy moments. The El and bus systems are relatively simple to sort out, and even have an online trip planner: http://tripsweb.rtachicago.com
Things to Do
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Check out 'Sue', the world's largest, most complete and most famous T. rex at the Field Museum of Natural History. You can check out various pricing options on their website here.
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Museum of Science and Industry - Adjacent to Lake Michigan, this museum features some cool stuff - a working coal mine, a German submarine captured during WWII, a NASA spacecraft used on the Apollo 8 mission amongst other things. Check out ticket prices here
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You MUST visit the Loop (Chicago's downtown area) to Millennium Park. It opened in 2004 and is a sensory overload. Check out Frank Gehry and Anish Kapoor's sculptures here.
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Take the Chicago Pizza Tour where Chicago is considered the Pizza capital of the world. A tour is available for May 30th priced at $36. Check out here for more
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Indulge in the zany with a Wierd Chicago Tour. Priced at $30, they offer a wide variety of tours from the usual Haunted House tour to the Al Capone tour.
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If you are a book lover do try Myopic Books in the heart of the Wicker district
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If you are in Chicago and you miss the view from Sears Tower, shame on you!
Do do do this!
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Ride the Brown Line El for the best tour of the city and its architecture!
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Play pool at the G-Cue Billiards and Restaurant. They even organize lessons!
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Visit Chicago Comics to get your fill of indie comics whilst you are there
Food
Check out this wicked NY Times slideshow on food in Chicago. Bon Appetit! I am recommending a few places based on reviews I am reading online:
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Cafe Jumping Bean - Try the latte here and you won't go away disappointed
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Vosges Chocolates - For that sweet tooth you mentioned. At Lincoln Park try a bacon-filled flying chocolate pig or a Chili brownie to get that right hint of spice in your chocolate
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Portillio's for the perfect Chicago perfect hot dog - ask for a Maxwell street Polish and you won't be disappointed
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Red Apple - For some awesome Polish food at $9.49 lunch, $9.99 dinner, $10.95 weekend
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Try Garrett's Popcorn (In the Loop) - They have caramel popcorn (with or without cashews or pecans), cheese popcorn, or a mix of caramel/cheese. Yum!
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For some French cuisine, La Sardine on the West Loop. On Tuesdays, you can choose any three courses on the menu for $25, and the food is excellent!
Use this link for figuring out places under $30 in Chicago which covers a wide variety of cuisines!
Suggestion: Try reading Nelson Algren's 'Chicago: City on the Make' which is a prose poem best read after the trip. It deals with the nitty-gritties of Chicago ever so beautifully.
NEW YORK
I wanna wake up in a city, that doesn’t sleep
And find I’m king of the hill - top of the heap
Frank Sinatra's lyrics speak of a city which doesn't sleep, where rags-riches is the norm and where everything is possible. The biggest city in the United States, the Big Apple as it is fondly referred to is a center for media, culture, food, fashion, art, research, finance, and trade.
FYI, NYC is divided into 5 boroughs with its own set of monuments and culturally distinct zones:
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Manhattan
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Queens
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The Bronx
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Staten Island
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Brooklyn
Tip: Get hold of a map of NYC - I think this would be very useful for orienteering yourself on locations, places and distances. Check this link for more.

Source:wwarby/Flickr
Things To Do
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Check out the Museum of Sex in Chelsea. It is dedicated to the he history, evolution and cultural significance of human sexuality. Check here for admission rates.
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Bike across the Brooklyn Bridge and take a ride on the Staten Island Ferry
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Stop at the Nintendo Store at Rockefeller Plaza. The latest games including downloaded versions of Nintendo games, and a downstairs devoted almost solely to the multiplayer uses of the Nintendo DS, the store should potentially blow your mind. Be prepared to wait in line for the fun to begin!
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Check out the Hayden Planetarium at the Rose Center for Earth and Space, located at the American Museum of Natural History in Central Park West. Check out admission rates here
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Pay a visit to Forbidden Planet, a fantasy land for alternative hobbies, such as graphic novels, comic books, manga and anime, and a wide selection of collectible figurines and toys
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And last but not the least please do pay a visit to the iconic Fifth Avenue Apple Store - the holy grail of all that is Apple

I haven't suggested eveything that are the normal tourist traps - Statue of Liberty, Empire State Building etc. I have found this link for you though which guides you to these kind of attractions. Hope this is useful.
Food
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For a prix fixe (A complete meal of several courses, sometimes with choices permitted, offered by a restaurant at a fixed price), Nougatine's has been recommended on Chowhound.
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Tocqueville's 3-course prix fixe lunch at $24.00 is the best luxury-dining bargain in the city
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S'mac - Well just plain macaroni and cheese, seems to be an icon in the Chowhound forums!
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Check out NYC's best pastrami sandwich at Katz's
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Quantum Leap for purportedly the best vegetarian burgers in Manhattan
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Apizz for that rustic Italian cuisine
Musical(s) in New York
I spoke to a cousin of mine who is native to Philly and she had 2 suggestions for you for which you can checkout the shows, reviews and ticket prices amongst others here
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Avenue Q - Showing from 2nd - 29th June, it is a racy but uproariously funny show. At Stage 3 on the New World Stages, tickets start at $104 onwards.
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Wicked - Not a musical and is the story of the wicked witch of Oz. At the Gershwin Theatre from June 1- 29, tickets start from $121 going all the way till $788.
Very Important Tip:
I think it is also important that you decide what kind of musical you want to see - whether you want singing, something with stage effects (Lion King for instance) or if you want something that is good and not necessarily popular or for that matter, something with a Hollywood star in it. If you decide that, I can also come back to you with much better recommendations. Will await your reply on this. 
Check out this Events listing of New York for June here.
If you need more information about travelling within Irvine, Chicago and New York, please let me know and I will be able to help you with that as well. Just let me know what stuff you liked from this list, so I know what works for you.
Have a fun holiday..Cheers
Kirti
PS: Thanks for the planner - it really allowed me to keep track of your time in all 3 places. 
NEW SUGGESTIONS FOR BROADWAY WITH CELEBRITIES
1. Promises – Promises – Starring Sean Hayes - $76-$300
Based on the Oscar-winning Billy Wilder film, ‘The Apartment’
Broadway Theatre, 1681 Broadway, New York, NY 10036
2. A Little Night Music starring Angela Lansbury and Catherine Zeta-Jones - $69-$214
Based on Ingmar Bergman's film ‘Smiles of a Summer Night’, A Little Night Music is set in a weekend country house in turn of the century Sweden
Walter Kerr Theatre, 218 West 48th Street, New York, NY 10036
3. The Addams Family starring Nathan Lane - $92-$315
The creepy, kooky, mysterious and spooky Addams Family comes to Broadway
Lunt Fontanne Theatre, 205 West 46th Street, New York, NY 10036
4. Fences starring Denzel Washington - $81-$191
The first Broadway revival of August Wilson's Fences as Troy Maxson, an African-American struggling with racial barriers, betrayal and his own disappointments.
Cort Theatre, 138 West 48th Street, New York, NY 10036
Note: All hyperlinks lead to reviews of the plays.
Hope this helps you make up your mind about which one you would like to see. I would recommend Fences if you are looking for drama and the Addams Family for more light hearted drama in that sense.