My favorite stay in Burgundy was Semur en Auxios. It's hard to pick, however, there is one beautiful medieval town after another.
I wasn't happy with Beaune primarily because my hotel wasn't good. I'd recommend staying either close to the big sights in the south half of town or stay well outside the ring road. The north part of town is pretty run down. Also have your lodging book restaurants for you. I found in Beaune if you don't need a reservation, it's probably a horrible restaurant. I liked the center of Dijon more than Beaune's center.
In Normandy, I particularly liked Fecamp. It has cliffs like Etretat but is more local than its more touristy neighbor. Bayeux is a nice small town.
In Loire, I was happy using Amboise as a base. It had a little of everything, chateaux in town and a small shopping/restaurant district. I also liked Chinon because it had a different (older) and authentic feel to it.
I very rarely pay anything close to 100 euro per night. I think the only place I've paid that is in Paris. Part of that is traveling alone (but most rooms are doubles) and part is because I travel during spring and fall when there are less crowds competing for rooms.