I would have suggested the Cote Basque (southwest) but there are not a lot of museums. You can do horse or bike riding, eat good foo as everywhere in france, there are castles... There are 3 major towns which are not huge cities : Biarritz, Saint Jean de Luz and Bayonne. And then there are a lot of little villages which are very cute like Espelette (french capital of pimento), Ainhoa, Anglet...
The whether is very nice in summer, the water temperature very goo and it's a beautiful region.
Nevertheless, you have to know that during the first week of august, there are the Fêtes de Bayonnes which attract a looooot of people from everywhere in france, it's kind of a week of a big party in the entire city with traditional songs, shows, ....
have a look to this website : http://www.tourisme-pays-basque.fr/
There is also Bordeaux and around. Museums in the city center and around , wine tours (léognan, pessac, cestas), castles in the region, horse riding not in the city center but in towns around like in Andernos, Arcachon (horse riding on the beach^^), then you can rent a bike in the town and visit besides taking the tramway, you could also go a day or two in the Bassin D'Arcachon (40 min from Bordeaux by the highway).
Bordeaux is a UNESCO city, the architecture is very interesting, it's a clean and safe city !
There are a lot of Restaurants Gastronomiques, wines of course.
If you want to relax an just do bike riding or horse riding, maybe visit one or two museums and an aquarium, not sure about the wine tours but you should go on the Ile de Ré. It's a beautiful little island where you can o everything by bike, still in the southwest, beautiful whether....
I'm from bordeaux so i can only advice you on what you can do in the south west, places where i've been... !
hopr you'll enjoy your trip !