Exploring the Dolomites for just a day

One good possibility is Ortisei, a very attractive village. I would say it was "bustling" in summer 2015. There's a nice, small woodcarving museum there, as well as the atmosphere to enjoy. The bus ride to and beyond Ortisei is scenic in and of itself. You will see mountains for sure unless you're unlucky with the weather to the point that visibility is severely affected.

am curious if there is more to see than ski resorts. We want to see the mountains, maybe wander a village.

Here is the deal. The villages are ski resorts, or more accurately, the villages become ski resorts in the winter. And mountains are pretty much required for downhill skiing, so they are right there. Yes, Ortisei is a good choice, or stay on the bus to Selva. The wall of the Sella Massif is right in front of you, and the Sassalungo to the right. You can get a walkers pass to ride the lifts up to nice restaurants on the mountain side. Rifugio Emilio Comici is my favorite. Check out the bathrooms, antithesis of the normal, less than attractive Italian loos.