To be right alongside the river Dordogne, for canoeing for instance, then try Camping Soleil Plage at Vitrac. Camping St Avit Loisirs at La Bugue is the sort of site to suit teenage boys, and Camping Le Paradis at St Leon sur Vezere is also great with canoeing directly from the site along the river Vezere. Sarlat le Caneda is the town 'at the centre of it all' in the Dordogne region, but is busy and traffic can be awful in high season.
When are you intending to go? July/mid-August are really busy, and sites may well be fully booked, so if you have a choice then after mid-August you should find space on most sites.