I visited Chenonceau, Amboise and Clos Luce in one day. I had a rented bicycle. I got up early and rode to Chenonceau. There's a good trail that starts at the west end of Amboise. The first mile (total 22km) or so is fairly steep up hill climbing away from the river. After that it's a nice ride in mostly gently rolling hills. There's a fairly long gentle down hill part, which becomes a fairly long uphill on the way back (then a steep downhill back into Amboise). Everything is paved and traffic, for the time you are on regular roads, was never scary.
I spent several hours there then ate lunch in a small town on the way back to Amboise. I turned in the bike then walked first to Chateau Amboise, then to Clos Luce. The only real problem was the grounds at Clos Luce were much more extensive than I had anticipated. I could have spent more time there than I gave myself.
I was there mid to late September and the weather was nice. Not too hot in the day and cool but not really cold at night.
Overall, it's very doable with a rented bike and reasonably sturdy legs.