Jackson and Telluride are two of my favorite mountains, along with Alta/Snowbird. But since you have such a nice chunk of time I think you'll enjoy being in a place like Telluride or Jackson more than Salt Lake.
I think I'd give the edge to Telluride. At one point Jackson was hands down the better mountain. But Telluride has undergone such an amazing expansion in the past few years that it now has an absurd variety of terrain for all levels. The old Telluride -- the Plunge, the Stairs, moguls as big as VWs-- still exists, but is basically irrelevant now. Gold Hill, Prospect, Revelation Bowl offer superb intermediate skiing, and there is even great beginner terrain lower down the mountain. I used to think of Telluride as Stowe in the West - steep, straight down the fall line runs cut through the trees. But now it feels like a European destination, with big open bowls, chutes, and hike-to and side country terrain in every direction.
What gives it the edge over Jackson in my mind is the convenience of the town to the mountain. Teton Village is a base area, not a town. Meanwhile, Jackson is really a small city, and it's a decent drive to the mountain.
But stay in the old historic town of Telluride, and you can abandon your car for the entire time you are there. All the restaurants, shops and lifts are all within an easy walk of most of the accommodations. The one reason to hang onto your car is that Ouray, Silverton, Durango, and, if you get some warm weather, the canyon country around Cortez, all make for awesome day trips.