For studio tours, check out the Warner Bros. Burbank Studios VIP tours.
Miceli's Italian restaurant has waiters who break out into song on and off, and they're not bad. A lot of waiters in LA are occasional/aspiring performers.
In Westwood Village, I can't resist getting a falafel pita with cheese at the Falafel King (although the old location decades ago seemed more lively/vibrant, kind of like the SNL "cheeseburger cheeseburger" joint... just reminiscing here).
Movie fans might also be interested in free screenings at USC, sometimes new films in advance of public release. You need to register, and show up a little early because they overbook. Look for "Outside the Box Office" here (https://cinema.usc.edu/events/
For amusement park fans, there's also Knott's Berry Farm (I haven't been there in decades).
Space fans might try the JPL Visitor Day Tour (I haven't), must register a few weeks in advance.
Those interested in witnessing the full spectrum of life in LA (underbelly, etc.) might like to take a look at Skid Row. I took a bus through there in order to meet a friend at Stumptown Coffee in the arts district and saw the tent city along the side of the road. Also, taking the subway (Red Line or Purple Line) in/out of DTLA is interesting if you want to see station interiors that resemble the insides of a sewer. The New York subway might have similar aesthetics, but they have a good excuse as theirs was built about a century before LA's was, and any deterioration is made up for in character. Can't say the same for LA. It seems somehow fitting that in LA, the sewer aesthetic is by design.
You may be aware that LA has a reputation for being a place for people who are pretty vapid and superficial (for example, Linda Ronstadt mentioned something to that effect, see her Wikipedia page). University life is, to some degree, insulated from the ills of the surrounding community, but still, I have the impression that UCLA is a place where it might be helpful to be more the "socialite" type going in. I spent a year in grad school there and left for other reasons than that (I was studying in a technical field and the studies in grad school leaned too heavily toward pure theory). Looking back, I think I might have done better if I had gone to UC Santa Cruz (or maybe Berkeley... but I didn't have the stellar undergrad GPA needed for that).
You might also try to find out more about the housing situation. As I recall, UCLA didn't have space for all the undergrads, so many have to live off-campus at some point.