When I lived in LA, my favorite ski area for a day trip was Mt. Baldy.
It'll be about 3 hours or so from you, I think. You'll need to check on that. It's a funky little area that gets good snow (or at least it did when I lived out there 10 years ago). There are few beginner trails, most are advanced runs, and you have to take a lift from the parking lot to get to the base area (usually can't ski down to parking lot, rarely has consistent snow on those trails). Most skiers were advanced and better when I went. Because of the higher-level difficulty of terrain, it was always the least crowded of the SoCal resorts. Views are great, too, if you care about that sort of thing. There is a gnarly access road, during storms you need to use chains. It's off the 10 and the 210. Here's the website: www.mtbaldy.com
For South Tahoe, I prefer Kirkwood and Sierra-at-Tahoe. Kirkwood has the highest base area of the Tahoe resorts, so it's snow is usually lighter and often more abundant (once you've skied in Sierra Cement, you'll know why they call it that!). The advanced and expert terrain is superb. Sierra-at-Tahoe is one of the "local" favorites and is known for its tree skiing. Not as challenging as Kirkwood, intermediates and advanced will be happiest here, experts might be bored after more than one day unless they simply love trees or venture through one of the five backcountry gates. Heavenly is nice too, but it tends to be more crowded--it's the most popular because it's the biggest and everyone's heard of it. You could probably find a cheap flight to Reno, then you can also choose from the North Tahoe resorts (since you don't seem to want to drive even as far as South Tahoe). In North Tahoe, Squaw and Alpine Meadows are best for advanced and experts.
Also, a trip to Mammoth is totally worth it.
If you'd like to read reviews and descriptions of what to hit on Mammoth and the Tahoe mountains, you can see my website, www.skisnowboard.com
(we don't review Baldy because we only cover destination resorts). Look at the resort's homepage and the mountain layout description to get an idea of the terrain on each mountain.