Question Paris, Loire Valley and Where Else?

We're heading back to France for the 4th time, starting and ending in Paris. We've decided to explore the Loire Valley for 4-5 days since it's new to us. We're not planning to rent a car, so we'll rely on private drivers and public transport. We're both in our late 60s, healthy, mobile, and love walking and immersing ourselves in culture. We're looking for suggestions on another town or city in this general area of France to spend 3-4 days. Any recommendations for places that fit our interests and are accessible without a car would be greatly appreciated.