If you enter the park via the "normal" entrance at Moose you'll head north and soon come to the end of the plowed road. The foothills just west and north of that parking lot are small, rolling, and usually have a number of well trafficed trails. A great place to wander, both on and off trail, and get used to snowshoeing. The views of the mountains are, on a clear day, absolutely spectacular.
Driving north and exploring the east shore of Jackson Lake is also very nice. Again, great views of the mountains.