For escape room, there's Real Escape Room LA in Little Tokyo, which is $35 per person for an hour and a half. Both
Escape from the Time Travel Lab (11 people) and
Zero Escape: Trust on Trial (9 people) have openings for the week that Espeonage is scheduled to be here, so pick the one that most appeals to you. Parking in Little Tokyo is about $10 for the day, so you can do your escapin' and get some nice eats in the area, all within walking distance.
To add to kanyeknowsbest's museum picks, there are:
- Aquarium of the Pacific - This is in Long Beach, which is a bit of a drive, but it's a place filled with fish and caters more to tourists; Cabrillo Marine Aquarium is better but smaller (also closer and much cheaper). $25.
- Autry Museum - If you're into learning about the wild, wild West, it's here along with the history of the area. $10.
- California Science Center - If you're a nerd and want to see a real, not-so-live space shuttle, there's one here. There's a lot of science-related exhibits here, too, if you're into that sort of thing. Free admission, special exhibits and IMAX cost extra.
- Getty Museum - Art museum. It has an amazing view of Los Angeles from the top of the Santa Monica Mountains. Free admission, $15 parking.
- La Brea Tar Pits - There's a large tar pit where they've excavated a lot of fossils and displayed them here. $12.
- Los Angeles Zoo - You can see some woodland creatures here and (a lot of) others, too. It's pretty nice now that they've finished most of the construction. This is a sizeable zoo, so you're likely to spend an entire day here if you're taking time to look at each exhibit. $20.
- Natural History Museum - If you want to see some dead woodland creatures and (plenty) others, too, they are here. They also have dinosaurs, but I'm pretty sure any natural history museum does. $12.
The Broad is a new art museum I don't know anything about, so I didn't include it. LACMA and MOCA are solid picks. I didn't list parking prices for everything, but paid parking is a given; the only free parking is street parking if there isn't a meter, and most of the places you'd want to be will be metered.
There's honestly a lot more museums and other tourist-type places to see in LA than can be reasonably listed here (e.g., Grammy Museum, Griffith Observatory, Petersen Automotive Museum), so if you spot something cool in a Google search or a city guide, go for it. If you like hiking, there's a lot of that, as well.
There's a lot of beaches here! Santa Monica Beach and the accompanying pier is fairly tourist-heavy, but it's a pretty nifty place to go if you don't mind that. The pier has an amusement park along with typical pier kiosk things, but the beach and pier gets fairly crowded on the weekends. It might be lighter in late October, but that really depends on how hot it'll be. There's also Malibu, which seems to be what people prefer. If you want to surf, I'll have to look up the hot spots, since it's been a while. Malibu also has a nice wildlife preserve if you want to check out southern California wetlands! Venice Beach is also pretty cool from what I've heard, but I've never stopped there. Marina del Rey, a little south of Venice, is a popular sailing spot.
Universal Studios Hollywood is in the Valley, which isn't that far from Los Angeles proper. They have that Harry Potter park now, so that's the place to be if you've ever wanted to be a wizard. Six Flags Magic Mountain is on the other side of the Valley (which itself is north of Los Angeles), but once you've driven all over the wonderful mess of urban sprawl, it's not that far. Six Flags Hurricane Harbor is also nearby if you prefer a watery experience. Weekends are quite bad for queues, though, but that's likely true of any theme park; you're probably going to spend hours queuing total for minutes riding total.
I'll add stuff to this post when I think of more.