The Loire à Vélo, the 900-kilometre cycle route that follows the river from its source to the Atlantic, passes right by the entrance to Villandry. Cycling between châteaux is the best way to do this part of the Loire Valley — the route is well signposted, mostly flat, and runs through villages and along the riverbank rather than the main roads.
From Villandry, Tours is 18 km east on the route (about an hour and a half of easy pedalling), and Azay-le-Rideau lies 10 km south. Bicycles can be rented in Tours and dropped at most of the larger Loire towns; many of the local hotels along the route will move your luggage on for you.