
I wanna wake up in a city, that doesn’t sleep
And find I’m king of the hill - top of the heap
Sinatra's lyrics applied to New York but in my mind, it works fabulously for Chicago as well. Chicago has heaps in store for any visitor coming into the city so I am going to make sure you don't miss out on anything whilst you spend your week in Chicago.
I am going to suggest on how you can travel around Chicago, what to do, where to eat and events for you at the time that you are visiting.
Weather
Weather is definitely not one of the attractions in Chicago. But the timing of your visit is just perfect. May is going to be pleasant and mild; June should be mostly fine too, although thunderstorms with heavy winds can also occur suddenly. So make sure you carry an umbrella along just the same. You can read more here for the weather forecast over the next 10 days.
Transport
The best way to see Chicago is by public transit. It is cheap, efficient and safe. You can use this link to plan your trips.
The Chicago Transit Authority, better known as the CTA operates an extensive system of trains and buses throughout the city of Chicago. Fares are paid with transit cards, which can be purchased and re-filled at kiosks in the lobby of every CTA station. Alternatively think about using the Chicago Card for the week that you are spending there. Or order yourself a Visitor Pass which you can use over 7 days.
There should be an attendant on duty at every train station. They can't provide change or deal with money, but they can help you figure out where you need to go and guide you through using the machines.
Buses
The best way to get around neighborhoods along the lakefront -- where the trains don't run -- is by public bus. Look for the blue-and-white signs to locate bus stops, which are spaced about 2 blocks apart. Each bus route is identified by a number and the name of the main street it runs along.
Once inside, watch the front of the bus — a red LED display will list the names of the streets as they pass, making it easy to stop exactly where you'd like, even if it's a small side-street. To request a stop, pull the cord hanging above the window and make sure you hear an audible 'ding'.
Rides of any length cost $2 with a transit card or Chicago Card, and $2.25 in cash. Major bus routes run 7-15 minutes apart during daylight hours, depending on the route.
There are several bus routes that are on a 24 hour/7 day a week schedule — these are called OWL routes, and the signs usually have an owl to make sure its clear to the visitor.
The CTA have a very cool CTA Bus Tracker and a CTA by Text applications which allow you to receive real time information on buses.
METRA
The Metra commuter railroad serves the six-county suburban area around Chicago with 12 train lines. But the Metra Electric, running close to Lake Michigan, will take you to Hyde Park. On weekends and holidays and during the summer, Metra offers a family discount that allows up to three children under age 12 to ride free when accompanying a paid adult.
Driving
Avoid driving in downtown Chicago if at all possible. Traffic is awful, pedestrians are constantly wandering into the street out of turn, and garages in the Loop can cost as much as $40 per day so my recommendation is not to drive but to make use of the good public transport system that Chicago has been blessed with!
Taxis
Chicago has some of the cheapest taxi fares in the U.S. Taxis are readily available throughout the major areas of interest for tourists and can be hailed from the street. The meter in Chicago cabs currently starts at $2.25 for the first mile and costs $1.80 for each additional mile, with a $1 surcharge for the first additional rider and 50¢ for each person after that.

Things to Do
We have answered customers previously on things to do whilst in Chicago whilst you are there. Read here and here for more.
To Eat
Chicago has neighborhoods that are known for their distinct style of food. Some recommendations based on what I have been reading online are as follows:

Events
There are a whole host of events happening in Chicago starting the weekend that you will be visiting so be sure to catch them.
Photographs
Check out these amazingly delicious looking food photos from the NY Times. Make sure you actually go and try all the stuff listed here. I guarantee that you won't be disappointed!

If you think you need more information on where you can get that perfect slice of pizza, where you can get the bestest view of Chicago etc, please do write back and I would be more than happy to help.
Cheers
Kirti