Bonjour.
The Loire châteaux are problably your focus in your Loire valley stay. You will probably visit all the major châteaux known to all, so I need not list the obvious.
In my experience, I can have 3 days of Loire castles. They are everything you dream. They deliver.
After 3 days, it's like having an overdose of the best pastries. Enough for me.
Among the castles, I especially recommend Villandry for its labyrinth garden and potager. Another intriguing castle is the castle of Amboise, for its Michelangelo heritage.
Chinon is a marvelously preserved medieval village, which I like as our base.
The Loire has other interests to offer: do check out a couple of the troglodyte villages, like Trôo.
Loire wines are also an unterrated great wine. You may want to visit a vineyard.
Where there are good wines, there is good food. I only remember Au Local and Charbon, both in Chinon.
If yo have a few days to spare, why not return to Paris via Burgundy? That would make a neat loop,
Burgundy is a beautiful region that is also underrated. It has much more to offer than its wines and its wines are fantastic.
A good base in Burgundy would be Beaune, with good eateries galore and great sites to visit, like the historical Hospices where the famous Burgundys auctions are held every year in the fall.
Our favorite stay is actually in a b&b right outside Beaune, in the winegrowing village of Pernand-Vergelesses. -- The b&b - La Maison de la Berthe has only one "room", but that room is a whole house. Upstairs you have your room your bathroom and a beautiful study with a Taiping rug that I want to steal. Downstairs are a large living room and dining room and basic kitchen. In the morning your breakfast is 100% homegrown: the eggs come from the one chick of the premise; the fruit and jam are from the orchard. Oh orchard, on nice weather, we install the table outside in front of the owner's potager and the unbelievable slopes of the Pernand-Vergelesses vines. The tiny village even has a one-star restaurant le Charlemargne.
Another great place to stay, not far from Beaune, in the cluster of all the world-famous winegrowing villages, is the Château de Mélin, with huge rooms and antique furniture. The châtelaine makes her own croissants every morning for the guests' breakfast. It also has its own wine cellar where you can taste the local wines.
The other places in Burgundyd that I love are:
Vézelay, the cathedral and the village, both breathtaking. And the whole area are charm itself.
A village that we like and always stop at is Noyers sur Serein, where we would hav a nice lunch at La Vieille Tour, a tuny jewel of a village bistro.
If you go Paris-Loire-Burgundyd, you make a lovely circle and never backtrack.