I've been playing a game called Ingress and it's got a lot of interesting ideas in it, because it's like a tour guide to public artwork. Here are some ideas for more apps, specifically around LA.
LA tour of the Mexcian-American war.
LA tour of the old Chinatown and the New Chinatown.
Something that lets you record audio at a location, and when someone else goes to that location, they can hear the audio.
The same thing for historic photos and photos.
The same thing for poetry and spoken word texts and written texts.
The same thing for music.