If you're extending your visit to Jackson, definitely spend a day on the river! Check out the white water (the Snake River has Class II and III rapids during regular season) or a scenic float in through Grand Teton National Park. Check out these guided options: www.barkerewing.com www.davehansenwhitewater.com Or if you're feeling brave you can rent your own gear at www.jacksonholekayak.com
JHMR in Teton Village has lots to offer even without the snow. You can take a scenic Tram ride, hike to the top of the gondola, or check out the mountain bike park. Teton Village has lots of great restaurants and live music in the commons most Sunday evenings in the summer time.