Among your first stops should be Colter Bay Visitor Center and Indian Arts Museum. Here, you'll be able to find your bearings and pick up some great ideas before you set out exploring.
You'll be spoiled for sightseeing choice when spending time in Moran. Colter Bay Visitor Center and Indian Arts Museum is a great place to kick off here, but there are numerous other worthwhile sights to appreciate. Grand Teton National Park, Jenny Lake, and Mount Moran are not far from the tourist information center and and will cap off your day nicely.