Oh wow! The City of Angels....you are going to have a whole lot of fun on this trip I can see 

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There is a whole bunch of stuff that you can do at LA so am going to recommend offbeat but also some popular stuff which would be a pity to miss!
Things To Do
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Check out Amoeba Music, the world's largest independent record store and a Hollywood landmark. Check here for reviews on Tripadvisor
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Take a yoga class at Golden Bridge Yoga (just off Sunset and Vine)
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MUST MUST MUST visit the Getty Center - Sweeping architecture by Richard Meier. The garden waterfall and azalea maze. Free entry as long as you don't need to park
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You gotta visit the Watts Towers- the neighborhood is no great shakes but they are one of the best outdoor monuments in the United States. They were built over a span of 30 years by an Italian immigrant called Simon Rodia. You can check here for more information.
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Walk along Venice Beach Boardwalk - the experience will be one that will last you a lifetime.
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Tar Pits in Los Angeles and I am suggesting you visit - Why oh why? Well because they constitute one of the world's best and most important sources of Ice Age fossils. Do visit La Brea Tar Pits for more.
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Experience a concert at the Walt Disney Hall, a testament of the Frank Gehry's architecture. Check the link out and be blown away by the architecture. I guarantee that you go in person and it will translate into an amazing experience. RECOMMENDED
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Museum of Jurassic Technology - Two of its most beloved exhibits are The Stink Ant of the Cameroon, an insect driven mad by a spore in its tiny brain, and The Horn of Mary Davis Saughall, an appendage that grew on said woman's head in the 17th century. Take this museum with a pinch of salt please

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Do a historical tour of LA with Los Angeles Conservancy - available mostly only on Saturdays and Sundays priced at $10 for non-members
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Drive along Mulholland Drive and check out the houses of the rich and famous. The views are to die for too!

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Food
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Apple Pan - RECOMMENDED - For that slab of grilled beef in a perfect bun and that delicious slice of fresh-baked pie.
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In-N-Out - RECOMMENDED - Founded in Baldwin Park in 1948 makes faultless burgers and fries
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Langer's at the edge of MacArthur Park since 1947- must try the deli's signature dish of thickly sliced hot pastrami on rye—washed down with a Dr. Brown's soda
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Try the Mexican at any of the restaurants at Olvera Street
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Rivera at 1050 South Flower Street in downtown LA - Food is pan-Latin American and rapturously good
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Pazzo Gelato in Silver Lake for totally amazing gelato
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Mashti Malone's in Hollywood. Homemade Persian ice cream and sorbets unlike anything you're likely to encounter
Whilst you are in Irvine, it might be worthwhile to check out LA Weekend happening May 21-22. Details are not yet out but keep checking the website for more information.
You can also check out Timeout's recommendations for 20 things to do whilst in LA
If you need information about travelling within Los Angeles do write back and I would be more than happy to help.
Kirti