Kurt, you have not said yet if you have a car too. To get the best answers, you need to say "I am taking the TGV from Paris and returning there after three days in the Loire." (Made that up, of course.)
That all is a factor in choosing a hotel location in a WIDELY dispersed area of many attractions. We stayed in an isolated, rural chateau-hotel, one which I do not recommend because it was a little disappointing, and very hot in summer, with no A/C. However, that was in 2012: Château de Marçay, 37500 Marçay - Chinon. One of the first things we did with our car was to drive to a "Target" clone and buy a 240 volt box fan!
Our small hotel hosted a commercial bike-tour for a couple of days, slamming the breakfast room. Ahem. But since you asked a question, I will mention that one place we visited for gardens looked very promising, and it's closer to the TGV stop you may (?) be using than are most chateau-hotels. https://www.labourdaisiere.com/en/portfolio-category/the-property/ It's also "centrally" located. I am not a biker, but I would not see the Loire entirely by bike. It's too BIG.