As you enter Besancon, you are warned not to park in the city so we grabbed the first parking lot we found, right below the citadel. We started the walk up; it wasn't too bad if you're a mountain goat, and it got progressively worse. The stairs are very steep, in poor repair, and have no handrails. We all made it up alive, but I was shot for about an hour.
Be warned, the restaurants are closed in the cold weather so you won't be getting any restorative tea or coffee. There is an information booth as you enter the compound and by the way, a very large parking lot, so don't make the same mistake we did, drive up.
You can spend the better part of a day visiting all the museums here. There is a permanent exhibit on Vauban and his work on the Citadel. There is the Franche Comte Museum which is a history and cultural museum. But what you really don't want to miss is The Museum of the Resistance and the Deportation. This is not a display for young children, however. It is graphic and extremely violent, as the times warranted. It details the French Resistance fighters and the violent end that many of them met. It also covers the Deportation of both Jews and Christians to the Concentration Camps of Eastern Europe. Very graphic and very touching.
For the children, though, there is a zoo, an aquarium, a Noctarium and an Insectarium. Certainly, plenty to keep them occupied.