Good plan. Lots of good info here. I live in PC and have passes to PC and Alta- I agree with the stay on the mountain advice- there's something magical about being on the hill. SLC is a city and prone to Bejing level pollution if you hit an inversion. Park City skiing is underrated by some but if you have a racing background the groomers are fantastic and plentiful. We had a pretty good winter last year with the best powder days since, what was it, 10-11? I had to shovel my roof twice that year. With the gondola combining PC and Canyons there's tons of great terrain. Jupiter Bowl and the back bowls at PC are very similar to the Cottonwoods and now, with the gondola, Pinecone Ridge is easy to get to. The least crowded terrain is farthest north, I'm told, but that's Canyons country and, with the connection coming in last year, I've just started exploring it. Avoid the Silverlode lift, which bottlenecks, and the crowds should be manageable. Although with Vail owning our mountain, we got a lotta Coloradans underfoot with Epic passes. Still, massive place, plenty of everything. The runs themselves are rarely crowded and a hundred feet wide- you can find yourself alone on a half mile long run and let the skis run. The lower altitude helps: PC 10,000', Alta 11,000 (top) but here's a tip- you can buy little oxygen cannisters at the RiteAid and, damn, will those come in handy for people coming from sea level, especially on a powder day moving fast.
Alta Bird is the queen & king of Utah skiing. I like to stay at the Cliff because it's affordable- The Alta lodges are rustic and expensive, I haven't priced Goldminer's but I checked Peruvian last winter because I thought I'd get stuck in the Canyon (snow) and they wanted $800 for a room. OK. Cliff isn't like that. It's built like the Wermacht's Atlantic wall because it's in Mt. Surperior's slide path, but if you don't mind concrete, it's great. The skiing is everything you've heard about. I prefer Alta to the Bird but others disagree. I did hit Mineral Basin (Bird) untracked last season with 18" of fresh and well... but if it hasn't snowed in a while the Bird's few groomers get pretty trafficy with SLC teenagers and boarders. (Two weeks of no new snow is why God made Park City) However, Alta is pretty much flat out excellent all the time. Lost count of last year's powder days.
Great dates- The Christmas crowds will all be gone and there's a very good chance for new snow. PC first to warm up, then Alta/Bird. Park City, by the way, is a very lively ski town with lots to do at night. Little Cottonwood Canyon's got no nightlife at all. It's all about the skiing. Take a walk and check out the stars... Great trip.