Well, depending on ho much time you have and how much you like to drive if I were you I'd consider hitting Yellowstone. I know, it's not in Utah, but from northern UT it is not that far and late May is a good time to be in Yellowstone for the following reasons: not yet crowded, still snow in the mountains, cold enough that you can get interesting misty conditions that can add a kind of etherial feel.
Some other ideas: Antelope Island (north od SLC), the Bird Refuge (west of Brigham City).
As to mountain views -- well they are everywhere and depending on what you're looking for can be viewed from your car nearly anywhere in the SLC/Park City/Ogden area.
Still, for me, I'd hit Yellowstone...
Brian