The centre of Tours is small enough to cover on foot — almost everything you'll want to see is between the Loire and the train station, no more than 20 minutes' walk apart. A single tram line (Line A) runs north-south through the centre, connecting the train station, the Hôtel de Ville, and the residential suburbs; a second line is under construction. City buses fill in the rest of the network and use the same ticket as the tram.
For chateaux beyond the immediate commuter ring, regional trains (TER) reach Amboise, Blois, Chinon, Azay-le-Rideau, Langeais, and Saumur. Bike hire is widely available and the Loire à Vélo cycle path along both banks of the river is the most pleasant way to reach Villandry, 13 km west.