We stayed at the Hotel Gustavia, conveniently located right across from train station. The rooms were very nice and spacious for a three-star hotel and were quite a bargain at appxly $75 US a night during the french school vacation week 2000 when the area was mobbed with people. If you stay at this hotel, ask for a room on the top floor, they have excellent views of the mountains. This hotel has a very rockus apres ski scene, so try to avoid getting a room on the first floor above the bar as these rooms can be noisy until the party quiets down. All other floors should be quite quiet.
My understanding is that if you stay at any of the local hotels, then you can use the local bus for free that picks you up at the hotel in the morning and goes to each of the local ski resorts; then drops you off back at the hotel at the end of the day. A very convenient set-up. I have not been back to Chamonix since 2000, but back then the lift tickets were a bargain. I think an all day ticket at Le Brevent was something like $18 US. We were able to rent skis, boots, and poles at a small shop in town just near the hotel for less than $15 a day per person.
I agree with RichardInSF that if you are a fairly decent skier that you should consider hiring a guide to ski the Vallee Blanche. It is an experience that you will remember for a lifetime. I also can recommend Le Brevent as a good area to ski.
I can't remember the name of the restaurant, but it was a Swiss restaurant on the main street in the center of the village. They had tasty fondue dishes and were not too expensive. There was a decent pizzeria in town too if you want something cheap and casual, forget the name but it was just near the center, I'm not positive but I think it was the only one in town. There is a wonderful little grocery store on the main street that has a decent selection of delicacies, chocolates, cheeses and wines if you want to take an apres-ski snack back to your hotel.