In Tokyo that would be the Apple Store. They have several types available to try. I'd drop a dime and see if that exists in La-La land too. Try the Shure 535's just for fun though. My personal favorite.
I'd think L.A. is probably one of the best places to do this. It might not be right around the block as it would be in NYC or Tokyo, but somewhere across the Southland, there's gotta be something.
That said, I'm not sure if anywhere will let you demo
earphones.
Headphones, yes, but do you really want to stick something covered in someone else's wax in your ears? No, and nobody else does, either, so I doubt there's much of a demand for that.
My Shure SE530s are the best 'phones, by far, I've ever bought (and I'd guess the 535s surpass them, but I haven't looked at those). My only complaint is their lack of durability--I much prefer the stiffer cables of the original E5 earphones that were available with the wireless in-ear monitor systems designed for live performances.