Actually the OP's plan sounds a lot like what I'm thinking about now (flying in, renting car, living cheap).
If you're skiing the SLC resorts, then Midvale/Sandy/Cottonwood area is the go. Lots of lodging options, plus the UTA ski bus services all 4 resorts via Fort Union area. Importantly, the ski bus runs on Sundays. Most UTA town buses do not run on Sundays!
Sundance is a wonderful resort but it's a bit of a drive, around in the canyon up from Provo. I skiied 2 days there, driving each day from Park City via Heber. First day I went back via Provo and SLC as the car had a flat tyre (space-saver spare!) and I had to return it to the airport. That was quite a hike. If you like ungroomed snow and a lack of glitz, it's probably worth staying somewhere a bit closer.
Snowbasin and Powder Mountain are also fantastic, but again a bit of a hike, out in the opposite direction (and not particularly near to each other, unfortunately). I always really enjoy Powder Mountain, and Snowbasin is quite an eye-opener since they tarted it up for the Olympics. Again, might be worth locating in a cheap motel a bit closer.
I'm still in the thinking-before-planning stage, and will probably be going mid January or thereabouts.