Take a boat trip round the Marais.
You can go to the 'Plan d'eau' which is an artificial lake to have a 6 km-walk. It's also possible to use your bicycle or rollers around it on a lane separated from the road - it's relatively flat.
In April, there is a music festival called 'Le Printemps de Bourges' where, during around 1 week, around 30 "official" concerts (prices varies) are given in the city (in several places, sometimes at the same time). The programme may be fetched in early March. During this period, most of the pubs and bars also have bands playing (for free) and the whole city gets a lot of animation.