First of all, Dockweiler Beach reservations can only be made 3 months ahead of time to the exact dates. They are now beginning to do June reservations so just be aware. Venice Beach can be done in the RV approx 24-27' (not TV with TT or 5th wheel). I wouldn't try any longer. I'd park on Washington Blvd near Via Marina. I would not attempt to get closer to the beach. Get there early before 9 am or parking gets more difficult. This gives you options to get out more easily. You can walk down Washington Blvd to the beach. There are plenty of places to rent bikes to ride. Venice Beach is nearby and Santa Monica about 3 miles on the bike path. Lots to see and take in!
I woulnd't do Downtown with the RV. I'd find open air parking and take the light rail into downtown or as others have said rent a car.
Dockweiler is noisy you get to hear and see all the planes take off from LAX, but closest RV park to LA in my opinion.