just have fun, like you would with your buds. it does depend on how well you know her, though.
amusement parks are great. you can't go wrong with this one, especially the really "scary" rollercoasters and the really intimate "it's a small, small, world", etc.
afternoon bbq's are also great, provided you're a bbq guru like me. bring the friends along too and get looped. do one of those seafood extravaganza's with the big pot o' lobster, clams, shrimp, etc. get your friends to chip in.
i'm a damn good cook, love to do it, and have fun with it. so, a dinner date at my place is always a good time. chicks LOVE a good cook and i score MAJOR points in this department.
Laker games! but don't get into the game too much. walk around, have fun.
in LA there are many "historic" neighborhoods that have guided walking tours--these are great--chinatown, little italy, etc...
go to a play or musical at your local elementary school! i'm talking 3rd graders. these are really fun and dirt cheap. there's no way she won't enjoy this. it's totally funny when they mess up. it's totally sad (well, funny) when they start to cry.
go to a palm reader or astrologist. chicks dig this stuff for some odd reason.
if you're near a big lake, rent a speed boat and go crazy. most chicks haven't driven a boat and they'll have fun--guaranteed. it's usually pretty cheap too. make a nice picnic basket and eat on the boat or on a private sand bar.
rollerblading at the beach. especially if she's never done it! you'll help her along, right? bikes too.
museums, art exhibits, festivals, the zoo, farmers market, are great too, and pretty cheap. Hollywood Cemetary is always fun. yes it is!
wine tasting gigs are a slam dunk. a lot of high end liquor stores have them, along with a nice dinner.
there are a lot of famous fast food places in LA, like Tommy's and Pink's. most chicks have never been to these places but have heard of them.
i have the bucks, and am getting my pilots license. so take her up in a plane on a clear day. in LA, you can do this for about $150 for one hour, for the both of you.
DRAG RACES! at the LA County Fair Grounds, there's always drag races going on--including amateur ones on weeknights/ends. you can even run your own car down the strip for a small fee. at some events, you can run a real drag car for like $50 bucks. trust me, you'll have a blast.
the point is for BOTH of you to have fun together. that way, you can't really lose. on the first couple of dates, just do something crazy and wacky, especially something that she's never done before and is exciting. plus, it take the pressure off, big time. you can make out later, right?
throw out some more ideas...