Kenko,
With just one day, and no car, I would look for a full day tour that would take you to 2 (possibly 3) chateaux, depending on how early you get to St. Pierre de Corps station. Chenonceaux is usually considered to be the one must-see chateau (for good reason). Or perhaps you could visit Clos Luce and 2 chateaux. Regardless, your best bet for transportation outside of Amboise would be an organized tour. I would hazard a guess that there are more than one or two on offer. I cannot speak from experience as we always have a car, but seeing two chateaux in one day is very doable, and three is doable also (some need less time to see than others).
Going from town to town or chateau to chateau isn't a walkable option for a day trip. Bikes/cars, yes; feet, no. The Amboise advice is good, but if you can find a way to see Chenonceau, do so. It is lovely!
Bonne chance!