Places out west I've been, ranked in order for a family trip:
Jackson Hole. The big one. Something for everyone. As extreme as you want to get. Has some good groomers, especially in the Casper area. Town of JH is fun, but a short drive.
Snowbird. No carving, but incredible if your family are expert skiers/riders. No town.
Aspen. If you can stay trailside at Ajax then great, otherwise stay at Snowmass. Buttermilk is nice if you want a large hill of green circles. Legendary town.
Steamboat. Something for everyone, great carving, great town.
Squaw Valley. Very little carving, but awesome otherwise. Terrain is up there with the best, but when I was there 22 years ago, there wasn't much of a town.
Park City. Something for everyone, large resort, nice town, not as "pretty" as the others. At this time of year the odds are that the only accommodations available are on the Canyons side. This is where we stayed, although nice I would not do it again. The best stuff is on the PC side, and it takes a while to get there and back from the Canyons.
I have been told I'd go nuts for the groomers at Sun Valley. It's on my list. Telluride is on my list too.
If your family is more intermediate level at skiing/snowboarding, I would put Aspen and Steamboat at the top.