Annecy and Chamonix are great but:
- both are busy in Aug, especially Annecy
- Annecy is a good 2-3 night stay, but 4 nights pushes it a bit and it's not great for day trips (slow roads along the lake, and the highway tends to bypass areas of interest - you could go to Chamonix for the day but it would be a bit rushed).
- Chamonix is far from Provence, and Chamonix to Lyon isn't that close either.
This does not mean that you should go elsewhere, but since you are looking for alternative suggestions, I would look into the Ecrins region. La Grave, a small village at 1,400m elevation, would be a great base for hikes, mountain excursions (there's a cable car whisking you up to a glacier at 3,200m), beautiful viewpoints (Oratoire du Chazelet ; col du Galibier).