I grew up in San Diego.
Rule 1. Don't leave a remotely attractive vehicle unattended south of highway 8.
Rule 2. Don't buy a fast motorcycle. You'll tip it over and sell it for half it's purchase price 6 months later.
Rule 3. Mission beach (the place Hornet is thinking of) is a great hangout day or night (lots of little restaurants and bars a bit away from the beach as well) but it's also a good place to get shot. If you go there, NEVER EVER drink very much because you need to notice when things are going weird so you can get out. Don't stick around to watch because every once in a while, gang wars break out there and sometimes you don't notice what's about to go down until you're in the middle of it. The one and only drive by shooting I've ever witnessed happened there. The shooter didn't hit anyone and only made one pass so most people were like LOL, but still the SDPD has to go in every year or two and clean it up when it gets too bad.
Go to the zoo and/or sea world. I think they still have military discounts. Definately a good place to take a date.
If you like scenic driving, head on up to Julian and over to Palomar observatory. If you can find Dudley's bakery, you've found one of Southern California's best kept secrets.
La Jolla is also a nice beach to hang out on. More huge mexican families taking up all the picnic areas on the grass there, but less gangs and just as many hot chicks.
Blacks Beach is still a nudie beach (IIRC) but it's not terribly interesting unless you just want to walk around naked. The strand off of Coronado also used to have a nekkid beach area but I think they shut that one down... Damn shame, they weren't causing any problems but the idiot puritans just gotta ruin every innocent thing that doesn't conform to their twisted worldview...
Ocean Beach is allegedly worth the trip to hang out on the boardwalk. It's a bit away from the base so there are fewer negative stereotypes of military guys up there.
Country bars in San Diego are a great way to find loose women looking for a man in uniform to use to cheat on their husbands. Many of those women are married to other military members. Occasionally you'll find one who isn't married and who just wants to find some young stud with a job to get them pregnant. Many of these women are pratically begging to get used, because they keep going back as if THIS time the guy will call her the next day. Avoid unless you really want kids or want to marry a country bar hottie who will then cheat on you in country bars the first time you deploy.
If you're interested in history, visit some of the old missions and Point Loma. Old Town is also interesting.
If you're interested in sea critters, go to scripps institute aquarium. If it's the right season, go on a whale watching or deep sea fishing trip (check with the base MWR or tours and travel folks for discount trips).
If you have money to burn, a trip to Catalina Island can be a fun way to spend a weekend. $$$$.
The gaslamp district downtown is a cool place to hang out. Horton plaza is right there, tons of restaurants, theaters, bars, etc. Something for just about everyone. They also have the convention center right there and there are concerts and stuff in an outdoor pavillion right next to the water.
If you want to see how rich people live, walk around La Jolla shopping and business district, starting from the La Jolla Cove parking area. Interesting. there is a great Thai restaurant in there somewhere near the antique stores, but of course it is expensive.
If you're into sailing or boats, I think the navy has a marina where you can rent boats. If not, some of the hotels rent sailboats that you can sail around mission bay. Jetskis are very popular, but check up on the local licensing regulations and rules or you could get a hefty fine for busting some stupid rule you didn't even know existed.
