I lived in Rennes for 5 months and had a great time there.
Nancy already hit on a lot of the great spots that are within a 3 hour train or bus ride. The Mont St Michel is a must. St-Malo, Dinan, Cancale, and Le Mont St Michel are all clustered together and it would be easy to include two in one day trip. Mix and match as you like. Nancy already mentioned the best spots for Normandy day trips so I won't repeat.
Since you have three weeks, I'll recommend a few places further afield (still within 3 hours). You could do a day trip (though it may make sense to stay a night...that's what I did) to Tours so that you can see the great castles in the Loire Valley (Chenonceau, Villandry, Azay le Rideau, etc). I had a great day trip to Concarneau where there is a castle built in the harbor. You could combine Concarneau with seeing nearby Quimper which has a cool half-timber town center with a grand cathedral. Well, it's far from the greatest cathedral in France, but it's probably the best one of all the destinations recommended here except for maybe Caen. If you can get yourself out to the Pointe du Raz, that's a great place to walk around on the peninsula when the weather cooperates. Windy days just make it more dramatic.
Have a great time!