Plenty of beach opportunities, obviously. The LA basin beaches might be just the ticket as they're easily accessible and usually only the surfers are out this time of year. Just south of San Clemente, San Onofre state park has some interesting sandstone-ish formations from erosion - reminiscent of much smaller scale Bryce NP (with the right light I bet you could make some stunning photos), a nice beach, and the "tits of California" <scuse my french ladies> - the San Onofre nuclear power plant. I've heard nice things about Dana Point, but never been to the beach.
As far as mountains go, there are actually a number of trails in nearby mountains. A few years ago I went on a hike to a waterfall (about 20-30 feet high in a nice little glen) and stream (yes, CA does have water) less than an hour from Burbank (probably under 2 hrs from Santa Ana). Not much in the way of wildlife, but pretty neat high desert type terrain, but with the added gem of water.
Mt Baldy, which is a ski area as well as a mountain, is just north of Upland (just north of Pomona) - I've never been up there, but should be good car access. Of course Big Bear is also beautiful, but that's a bit more of a hike.
I've also been exploring (but this was 15 years ago) in the mountains just north/west of El Toro. If I remember correctly, Saddleback mountain is up in that area (possibly even in the Santa Anas) and might offer some interesting scenes. I used to go trout fishing within 15 minutes of El Toro, but I'm afraid I don't remember how to get there.
San Juan Capistrano (where the swallows return) was always talked about when I lived in El Toro, but I've never actually been there myself.
Don't waste your time on Lake Elsinore if you're looking for scenics - it's really a biker haven.
Overall, I'd say your best bet for 1-2 hour trips would be San Onofre, the Santa Ana or San Bernadino mountains. I think Big Bear and other areas up near San Bern. would probably take you 4-5 hours, but Big Bear is probably worth it - the drive up is pretty scenic on it's own. I think Joshua NP is more of a 2 day trip, while you could do Big Bear there and back in a day, including sunset (but you want to be on the beaches for sunset, right?)
One suggestion for you is to contact some mountain bike shops or web sites - people don't realize it but there are tons of trails in the mountains surrounding the LA basin, oftentimes very close to civilization (like Pasadena or Diamond Bar). LA is HUGE geographically, so good luck.
Oh yeah, why not check topo maps? Might give you some ideas.
Oh yeah, don't forget about LA and San Diego zoos if you're into that captive wildlife thing.