L ' E t o i l e A r g e n t é e has much to offer in the vicinity
At 100 meters there is a swimming pool (open in summertime) and a tennis court. From L'etoile Argentée you can make beautiful walks or bike rides and there are possibilities for horseback riding.
Saffres, (5 km) is a famous climbing area. A large lake with beaches is located just south of Vitteaux. Closer is the Canal de Bourgogne with possibilities to rent a boat and explore the area from the water.
There are 2 golf courses within 15 miles and several rivers where you can fish.
More information can be found on the website of the office de tourisme of Vitteaux.