IMHO, downtown L.A. is a super dump. There is not much to do and no reason to stay there.

For a tourist, the main attraction is the Disney Hall, which is worth seeing (nice cafe inside, too). It is near a subway stop.

I suggest Santa Monica (near 3rd St Prominade) or West Hollywood area. Beverly Hills is okay, but be sure you are in the downtown area of BH (which is not a dump).

When I moved to L.A. I couldn't believe that you really, really had to have a car to get around. Now, I believe. But, you can see a lot via bus and the limited subway.

See the Tar Pits for sure. Amazing! And go to Farmer's Market at Third and Fairfax (this is not the same Third St as the one in Santa Monica). Getty is well worth the trip. And is free if you come on the bus. Check out the L.A. Weekly (comes out on Friday) which is free entertainment paper.

Forget taxis. Really doesn't work in L.A.