Loire Chateaux west of Tours

Chateau Villandry: https://www.chateauvillandry.fr/en/

There are a number of interesting chateaux west of Tours. Villandry, Chinon, Azay-le-Rideau, Langeais, and l'Abbaye Fontevraud, just to name a few. (Fontevraud is interesting although not actually a chateau). There are also the chateaux at Saumur and Angers, which should be accessible by train since they are in cities. So, no shortage of possibilities but I don't know about reaching most of them by train. You can check schedules at the French rail site https://www.sncf.com/fr
An equally important question for you is which will be open when you'll be there.