Going to the zoo is only by bus or taxi. Same with Sea World, and most of the buses stop running after 9:30. There are a lot of transients at Old Town trolley stop and some of the downtown stops. Daytime is pretty safe to get around, but know the routes. The zoo and Sea World are on the costly side, but you_ll spend a full day doing things.
Amtrak to Union Station LA is 30 bucks each way. Unlimited subway is about 3 dollars, but there_s plenty to do in the area.
You can get a 3 day ticket at the trolley stop, which covers buses too.