I went to go check out the FIDM costume exhibit and it's definitely worth a stop for screen-used costume enthusiasts in the LA area, and admission is free! FIDM doesn't have a large exhibit space but they have a good representation of costume designs from movies in the last couple of years, like Alice in Wonderland, Immortals, Super 8, Thor, Captain America, Cowboys & Aliens, War Horse, and Hugo, to name a few.
Info here: http://fidmmuseum.org/exhibitions/current/
Exhibit ends on April 28.
Unfortunately no pictures are allowed in there so I can't share anything but I did manage to get really good looks on the Cap, Thor, and Loki costumes, spent most of my time checking those out because I'm a Marvel geek. I'm still trying to get over how the hero Cap suit auctioned for over $200K But seeing the Cap costume up close did give me a better idea for my own TFA outfit. The Thor and Loki costumes are absolutely stunning, blows most of the other costume work in the exhibit out of the water.