We've always had a car, so I wouldnt know about bus trips etc. There is a really good tourist office right in the centre of the city that has lots of information.
Just in Granville: there's the Christian Dior museum and gardens, a trip to the medieval old town where there is a museum, cathedral and an acquarium, a casino, a beach with an outdoor swimming pool, the walk along the mur d'atlantique, day trips to the jersey/chausey islands, lots of nice little boutiques, a market on saturdays and often antiques markets too. There are some great restaurants esp if you like seafood. I love having moule frites with a glass of chilled muscadet- cheap as chips but fresh and delicious. That's just what I can think of offhand
With a car you could go to: Le Mont St. Michel- I would highly recommend this, utterly gorgeous place, but very crowded in summer, fantastic off season. There are lots of nearby seaside towns like Agon Countainville, Regneville, Donville les bains and in the other direction, Jullouville, St Pair sur Mer. There are lots of activities in these places, depending on what you like- but you can rent bikes, go horse riding etc. There are the old fashioned rosalies- the four seat bikes too which are funny. Lots of brocantes, antique shops, cafes and restaurants.
There are many WWII museums along the landing beaches of normandy too. There is a nearby zoo in Champrepus, and I know there are quite a few big parks and gardens around too. There are many other attractions, too many for me to remember here, but the tourist office there has ( in every language) information on every thing.
Everytime we go we go to the Herel ( Ibis) for a coffee in the morning and pick up a copy of Ouest France( local newspaper) which has a section on what is going on around the different Normandy every day and tend to check the weather and work from that.