See a show at the PAC; we've got Broadway stuff, people!
There's a solar observatory, since Big Bear gets an average 300 days per annum of sunshine.
Ski at Summit, board at Bear. One lift ticket is good at both mountains. Get there early, or you're in for a hike or a cold shuttle ride.
Quick Tips:
There are three ways to reach Big Bear: Highway 330, the front way; Highway 38, the side way; and Highway 18, the back way. Most people take the front way through rim of the world. This is not the best way! 330 is one of the deadliest highways in the U.S.; it has rock slides, and the curves are dangerous.
The safest way is up the 18. You only have 20 miles of mountain road, and it has very few rockslides. Come up using the 15 to Victorville, then Bear Valley road into Lucerne Valley, hopping on the 18 for your mountain ascent. The best thing about this route is that you get a lot more "civilization," i.e., gas stations and fast food joints. But if you want scenery, take the 38! It's safer than the 330 too.
Don't rent your equipment at the resorts! It's a lot less for the same thing at the rental shops throughout the valley! There are lots of places to stay; your best bet is probably renting a house. It works out to about half the price of a hotel. There are lots of agencies that handle house rentals up here.
Best Way To Get Around:
The main road through the valley is Big Bear Blvd, which has just been repaved (oct '05). We've got a bus that goes "down the hill" twice a day and a nice visitor's trolley. Walking around town's not really feasible since the valley is very long. We've got two car rental places: Enterprise on the Blvd and Airport Rental at, you guessed it, the airport.
It's a small plane-type airport, but it does have some charter service, and that's only a half hour to LA! There are a couple of taxi services, but your best bet is to bring your car, preferrably a nice 4x4, so you don't have to buy chains. (The restrictions rarely go beyond R2-chains unless it's a 4-wheel-drive, so you probably won't need chains if you bring a 4x4.)