Hanover itself is very walkable. The campus, Main Street, and most restaurants and shops are within a ten-minute walk of each other. A car is not necessary for anything in the village center.
The Advance Transit bus system provides free service throughout the Upper Valley, connecting Hanover with White River Junction, Lebanon, and other nearby towns. Routes run on a schedule — check the Advance Transit website for current timetables.
For the surrounding region — covered bridges, state parks, the Connecticut River — a car is more or less essential. Rideshare apps work in Hanover, though response times can be slower than in a city.
Cycling is reasonable within town and along the river, though road shoulders are narrow on many routes.