Nevils:
I agree with most of what Colin said.? Snow Basin and Powder mountain are two of my favorite Utah places, but we have never stayed in that locality.? We have stayed in Park City (about an hour drive), at a place near a lake about half way between the two, and in Salt Lake City itself.? One of the attractions of Utah is the fact that everything is a 30-45 minute drive from Salt Lake.? We seldom ski much more than 2 days at any one place out of a week stay.? I've never been in the Columbine Inn, but it's not impressive from the outside.? More importantly, I don't think Powder Mountain has enough terrain to ski multiple days there (but I love the ambience there and won't visit Utah without at least one day at Powder Mountain).? We also didn't find the drive up the mountain that intimidating, so a slight disagreement with Colin there.
Snow Basin is really well segregrated, with more expert terrain to the right and easier to the left (and Strawberry Bow is just awesome).? Lift ticket prices there are comparable to park city resorts, but I've yet to see it crowded there. Powder Mountain is more in the Alta price range.
Don't know that there is any way to determine the best one week way in advance, but I would consider later in February or even into early March rather than in January.? That's a little safer, although they have had lots of early snow for the past of couple of years.? I've been there in earlier January's when the snow was skimpy (by Utah standards) and I was there in April in 2000 and had great snow.? Note also that Powder mountain doesn't do any snowmaking (most of the name resorts do), so factor that in.