L.A.'s got tons of stuff for you to do even as a minor. As mentioned already, Santa Monica's got some really neat stuff to do and look at around the pier. It's probably too cold right now to go boogey boarding(which is a blast), but I bet the Santa Monica Pier would be open, where a few rides are(roller coaster, and the famous ferris wheel there. Absolutely great view of the ocean when you're on it). Also you can see all the famous sites around there from movies, like that outdoor gym right on the beach where all the bodybuilders work out(I think that's Venice Beach. Its all attached though, you just keep walking and it goes from beach to beach to beach), and theres a skate park which always has some awesome skateboarders doin their thing and attracting a big tourist crowd. There's a big path going around all the beaches so you could rent a bike or even some rollerblades and check out all the beaches in a way that wouldnt take you all day.
Hollywood's also alot of fun. Walking along the Walk of Fame - or whatever that sidewalk's called with all the stars on it - is interesting. And the Hollywood wax museum was pretty hilarious too, if you've never been. Some of the wax figures look really good, almost creepily good, and others looks just awful, which is good for a chuckle. I think its like $7 or $8 to get in. There's also a huge outlet mall just off walk of fame. I can't remember the name but Im sure you could find it pretty easily from there, its maybe a 5 min walk going uphill from the walk of fame. Lots of brand name stuff at cheaper prices, and some cool restaurants in there to chill at, and have one of their micro-brewed b...er...soda pops
Also in Hollywood is the Hollywood Hills. If you are able to go in there(I know it may be tricky since it sounds like you wont have any wheels), you can go up to the famous Griffith Observatory, which overlooks the whole city, and its in the same area as the "HOLLYWOOD" sign, you can totally see it. Its a trail around there so you can walk all over, plus get some nice views of downtown L.A.(if you can see it through all the smog, seriously). And again, if you do have wheels once your parents get there, cruising in that area is fun, as its where all the movie stars live. You can't get too far in - there's security - but you can still see alot of the movie star homes(I'm not talking about that tour bus strip. I mean when youre actually deep in the hills, in their residential area).
Something else which we did that was alot of fun was took in a TV taping. Me and my buddy went to a taping of That 70's Show, it was pretty cool(Fez is a total pimp btw, I swear Donna wants to nail him, she was giggling over him between every take. And Jackie's even hotter up close). Its free to get in, though you may have to wait in line for a couple hours to make sure youll get a spot, as the lines fill up pretty quickly. But you cant just walk in off the street, you have to get it arranged a few days in advance, along with a copy of your driver's license, so they can check your record and make sure you're not some crazed lunatic who's gonna attack one of the cast members or something. My buddy did it for us, I dont know how but Im sure you can find out pretty easily. I dont know if that was just for That 70's Show or if they all do that, but it seemed pretty straightforward and simple.
One last thing Ill mention is to go to Rodeo Drive in Beverly Hills. For the most part, stuff is WAY too expensive to buy, but its a cool little area to walk around in and poke your head around shops. Its mostly tourists anyways, so its not like youll stand out or anything. Then afterwards you can cruise around the Beverly Hills and check out all the crazy houses on the main drag leading into the city, some of them are absolutely unbelieveable. And pretty original looking too, some people have put some very interesting, expensive add-ons to their house(probably knowing they're living on a drag where tons of tourists cruise by to check out the houses)
LA's a really cool place to hang out in, even if you're not of age. Since you're out in Anaheim, I dont know how practical it is to get to all these places I mentioned, but I thought I'd at least give you some suggestions about stuff that we did when we were there(we stayed in Hollywood and Santa Monica though, I'm not sure how far out Anaheim is but Im sure its a ways, LA's huge). If I were you I'd definitely go early, it'll give you a chance to kinda see the city at your own pace and see all the things you wanna see, before the fam gets there and its compromise city(gotta love those fam trips

). I'll stop here because this is getting pretty long, but if I remember anything else thatd be fun for you to do, Ill post it.