UNR checks all the boxes. It’s 25- to 45-minute drive to a half-dozen ski resorts. And if your kid is interesting in more serious alpine pursuits (e.g., ski mountaineering), the Eastern Sierra is a 2- to 4-hour drive, and it’s as good as it gets. UNR now offers students the option of living and studying directly in Tahoe for a semester or year: https://www.unr.edu/lake-tahoe. It’s also good for all the other outdoor activities mentioned.
My other thought was the University of Utah. It also checks most of the boxes. That said, Salt Lake City is now somewhere between a big city and a massive suburban sprawl.
I love Flagstaff, and it’s great for general outdoorsy options. But I wouldn’t go to NAU if skiing is a priority. Ski Bowl is the only real option, and it’s okay at best.