If you have a group, it is fun to rent a house at Alta. If not, the nicest place is probably the on-mountian hotel at Snowbird, the Cliff. Very cool architecture, nice amenities, etc if that is more your thing.
The budget route is to stay down in the valley. If you don't have snow tires, you can park at the base of the canyon and take the city bus the last few miles up to the resorts. Be aware that on snow days they do avalanch control and snow removal in the early morning and afternoon so the canyon gets closed at times.