Here's my suggestion:
Split your stay up. Spend half your time on the south shore and the other half on the north shore. On the south shore, I recommend staying at Harvey's Casino and Hotel. We stayed there in 1999 and loved it. They included an awesome buffet breakfast with the room price, which was served in the dining room on the top floor with great views of the lake. Shuttle buses pull right up to the hotel, so you don't have to slog your equipment to a bus stop. There is also a new gondola to Heavenly right across the street. The room was sweeeet: marble tile, tv in the bathroom for viewing while soaking in the tub, separate toilet room and shower stall, big room, big, comfy bed. On the north shore, I'd stay in Squaw Valley or at Granlibakken. If you can swing it, the Resort at Squaw Creek is ultra deluxe, with its own chairlift. There are other, less expensive places in Squaw Valley as well; www.squaw.com
has an accomodations link.
Also, I'd really think about renting a car while there. My friend and I stayed there for a week two winters ago and rented a subaru outback. We drove to Heavenly, Kirkwood, Alpine Meadows and Squaw and a great part of the fun was the beauty of the drive around the lake, stopping at local diners and scenic overlooks.
Finally, look into a multi-day interchangeable lift ticket which is good for all the big ski areas at the lake.