Built along the Garonne river, the historic part of the city is found on the left bank. If it feels like a mini Paris, you wouldn't be mistaken. 'Modern' 19th century Paris was modeled after 18th century Bordeaux. Even the Paris Opera was inspired by the Bordeaux Opera house. My favorite area to wander is probably along the narrow streets between the Grosse Cloche and the Eglise Saint Pierre. It's a great area to wonder around and find some of the old Medieval buildings on streets with names like 'Rue du Loup', named after the trades of people who used to work on them, in this case selling wolf skins. You can taste historic dishes like lamproie a la Bordelaise at the oldest restaurant La Tupina or more modern and unique meals at chef owned restaurant C'Yusha.
There are unlimited amounts of things to do with children in this area, from beaches to parks and museums. It's a very family friendly area, with lots of great camping grounds in all price ranges (the French version of a holiday home/camping/vacation park). Most larger French towns have a beautiful old carousel which kids adore, good parks and public pools.