You're probably going to need to provide some more details in order to get the answer you want. What kind of touristy stuff do you want to do? Where do you want to spend your day? Will you have a car? It's a big town, so if you've only got one day, there is only so much of it than you can/should cover. Is price an issue?

The two areas that immediately come to mind for me are the West Hollywood/Sunset area and the Venice/Santa Monica area. It all depends on the vibe you want.