Find Jonathan Gold's list of 99 best restaurants in LA. They vary widely in price so there's something for you no matter what you want. He's the best food critic ever and though I've had a couple of misses if you just start going to the restaurants on that list you will be happy.
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about walking and go on the tours. Lots of history there and even though you look like an idiot tourist it's a great way to figure out sections of town you never knew existed.
-Michael