I have two daughters and at that age the theme parks were a big hit. Universal Studios and a Disney park would probably be the places. Perhaps you could take one of the daughter’s friends with you. However make sure they are OK with being away from home and make sure you get a signed permission note to cover you and if an emergency comes up.
If you’re hitting LA the beach may be a good place to go. I would also recommend getting tickets to the taping of a TV show. A kid’s “Giggle Show” would be of interest to your daughter (she’ll see her TV stars) as well as you (if you’d like to see how a show is taped.”
I’ve never had good luck with double vacation with another family. Little things like: “Why are they always late” and “I wanted to stay at that place longer” or “Why must she always yell at her kid” always seem to come up.
I always try to do out of the ordinary things. Maybe a whale watching trip if you’ve never been to sea, a mountain trip if you never see snow or maybe 4 wheeling in the desert it you’ve never been.