Greetings Pekin, welcome out west.
Happy birthdays to everyone. Should be a fun holiday. You are coming into town during the shoulder season, in between the peaks of summer and the upcoming ski season. All of the fall colors will be gone, but there likely won't be enough enough snow for a horse drawn sleigh, snowshoeing, snowmobiling, tubing, etc. You could find an outfitter for a hot-air balloon ride. You cold also check into taking a ride on the mountain coaster at PCMR or the bobsled run at Utah Olympic Park.
The obvious choices are a gallery and shop stroll up Main Street. The Egyptian Theater is where they have a constant line up of Sundance Film Festival screenings every January. Robert Redford is the owner of Zoom restaurant, near the bottom of Main Street and Danny Masterson is the owner of Downstairs nightclub. Try High West's blackened cod. Friends from NYC and LA said it was the best meal they've ever had. Chimayo is great Southwestern food. You may be able to find significant savings in local newspapers and magazines for dining options because there typically aren't many tourists in town during this time. The restaurants want any business they can get.
You should also check out the Utah Olympic Park. There is a museum and with the right timing you could watch Olympic athletes training. You may be able to take the Red Pine Gondola at The Canyons Resort for some nice mountain views. Once you're up top there is a lodge and possibly other activities.
If you like shopping there is the Tanger Outlet Stores with brands like Ralph Lauren, Banana Republic, etc. There are also several spas to choose from resorts at The Waldorf, Montage, or St. Regis to Main Street locations like Mountain Body.
You could always do a day trip a half hour away and spend time in Salt Lake. Check out City Creek Center and Temple Square. For a fantastic view of the mountains take a ride of the Snowbird Tram. There is a warming hut at the top of Hidden Peak, but make sure you bring a winter coat, gloves and a hat. Or you could check out one of the new museums like the Natural History Museum, Leonardo, or UMOCA.
Hiking is always an option, though it will be weather dependent. If it has snowed and melted the result would be trekking through mud. There is a nice boardwalk around Silver Lake, if Guardsman Pass is still open into Big Cottonwood Canyon. Again, dress for winter conditions.
Here is a nice guide for PC. There is an events calendar and other activities to look through.