Regardless of where in town you choose to stay, it's pretty easy to get around town. City shuttles run daily around town and to and from Main, Eagle and Canyon lodges. The Village is a central hub for all lines, green, red and blue. If you choose to go out at night, the shuttle run until about 1 am.
From the L.A. area it's about a 6 hour drive (+/- 1 hour depending how fast you drive). There is an aiport, but I'm not sure it provides commercial airline services.
Being from L.A. I drive, of course. Going to the ski lodge, there are shuttles. Depending on where you're staying, you could even walk to the lodge. Walking to the stores is possible also, depending on where you're staying and the weather.
The town of Mammoth Lakes provides free shuttle service for getting around town and to and from the Mountain. They run pretty often and have racks on the sides for carrying your skiis or your boards.