Keystone has an excellent and reasonably affordable Nordic center if you are interested in using their facilities, but there is also good snowshoeing right along the small Snake River. This short and easy trail wanders along the river behind some nice homes.
Parking near the start could be an issue for you, but if you solve that problem this is a great scenic snowshoe hike. If you don't have a car spotted at the other end, the best place to turn around and head back is at the science school. In fact you might be able to park just outside the science school and begin your trip from that end, avoiding parking in the neighborhood. It all depends on what you can find and what the snowplows have been up to.