Within the region, Albi is the obvious one. A brick cathedral the size of a fortress, a compact old centre, and the Tarn running underneath it. Uzès and Pézenas do the same job on a smaller scale, and both are close enough to visit from here rather than move to.
Over the border, Girona is the closest Spanish equivalent: walls, a river, a dense old town and the Costa Brava within reach. The drive is under three hours and the change of country makes it feel further.
Further afield the pattern still holds, and the best examples of it are rarely the famous capitals. What makes a week work is a walkable base with a dramatic backdrop and enough nearby day trips to fill it. Cape Town does this as well as anywhere: Table Mountain instead of the Cité walls, wine country an hour out, a coastline and a boat to Robben Island. If you are weighing that kind of trip, a good area-by-area guide to where to stay in Cape Town is worth reading before you book, because the difference between neighbourhoods there is larger than it looks on a map.
The common thread is scale. Somewhere big enough to have proper restaurants and a market, small enough to cross on foot, and close to something you would travel to see on its own.
What does not work, in our experience, is a beautiful village with nothing within an hour of it. Three days is lovely and the seventh is long.
