You tell me man. Mostly want to make it a food and booze trip. Palm Springs for a couple days for spa/golf stuff, and Joshua Tree with a camper van for hippie shit. Where in and around LA should we hang out?
If you want to do a romantic, semi-tourist trap, either eat dinner or gets apps and drinks at Yamashiro. It's the pagoda above the Magic Castle, you can see from Dodger Stadium all the way to LAX. There's a koi pond and the waitresses are dressed in amazing kimono.
Do not get sucked into the Farmers Market. Overpriced and not much there. Don't go to Pink's. Their hot dogs are mediocre at best.
palma will know more about the current foodie places in LA proper.
Some fun just drinking and goofing around could be going to the 3rd Street Promenade in Santa Monica and the pier is a couple of blocks away. There are several bars on the promenade (but some of the best are dive bars walking in the neighborhood), street music.
If you know when you are arriving, you might be able to get tix for Conan or other shows.
The Getty is an amazing museum and has incredible views (you have to make a reservation for your car)
EDIT: If you liked, Once Upon a Time in Hollywood, the restaurant they kept showing was Musso & Frank. It's old, old, old school Hollywood. Food is OK, pricey, but is is stopped in time. The Palm is the Palm wherever you go to one, but this one has lots of famous people. When their Maitre D' died, BH police said on Sinatra's funeral was more attended. If you go to The Palm, you can go to a show next door at The Troubador.