There aren't a whole lot of towns right off 395 that aren't quite a bit closer to Mammoth than LAX (Lone Pine is about two hours from Mammoth.) So I'd say Lancaster/Palmdale, with a leaning towards Palmdale as it's a little nicer area. That'll get you about 90 minutes from LAX (CAVEAT: Traffic!) If you're flight is on 10:30 on a weekday, you WILL hit traffic at peak morning rush on the way down. There are a LOT of folks who commute that far into L.A. if you can believe it. The 405 BLOWS! So be prepared. If you are driving back on a Sunday it shouldn't be an issue at all. Saturday probably won't, either. (Did I mention the 405 BLOWS! My husband drives it every day. I avoid it as much as possible.)
I got an email from Mammoth that they are running some lodging specials. The Mammoth Mountain Inn, which I have never stayed at so can't give a yay or nay, is slopeside and next to Main Lodge so it would make your day very simple. The downside is it's isolate from the rest of Mammoth Lakes, but there is a place to eat and down a few beers there (the Yodler--fun place.) I think the Inn also has a restaurant. If you have a car which it sounds like you will, you can venture the 5 miles down the road to the main part of town in the evening if you're so inclined. If you don't care where you rent (meaning you plan to ski the same ski the whole time) and don't care about slopeside, then you have a plethora of options. If you stay at the Shilo Inn, it's right across the street from Footloose Sports, which is a great place to rent/demo, including boots (they have demo boots.) You can then hop a shuttle to the mountain. There are different shuttle lines throughout town that service specific areas, so you'd have to look into where each one goes, but I don't know that there's a better or worse place to start your day (Canyon vs. Main vs. Eagle.) They'll all get you on the hill one way or another :D
Can't believe I'm the only one piping in here! Everyone else must be lucky enough to be up there this weekend.