One thing not mentioned yet is that Annecy is a great town and area to explore by bicycle.
The multi-use path around the lake is mostly flat (pretty much completely flat on the west side, with two decent climbs on the east side) and is well maintained. The view from the path is excellent, and the people on it are mostly well behaved (save for commuter rush hour when it can get busy). Plenty of beaches, cafés, and the like are directly on the path. Of note is Le Bon Wagon in Duingt, which is a bike shop with an excellent café - really great.
I know that moving under pedal power is not everyone's cuppa, but it's really a big upside for Annecy.
I've been there in June, July, August, and September. The June and September visits were the least tourist-laden, for sure. The Fête du Lac, on August 1, is always awash with tourists as it's one of the largest fireworks displays in Europe. And yes, it is the kind of old town that is social media friendly. But it's a real town with locals who know how to exist happily during peak tourist time. That's been my secret, as a high school mate has lived in Annecy for nearly a decade and knows the ropes of how to get around the glut of tourists - knowing that sometimes, regardless of season, it's unavoidable.
Obviously I love the place and would go back anytime.
And I agree about Chamonix, though it can be pretty saturated with tourists during both peak hiking and winter sports seasons. Luckily the French Alps are awash in lovely mountain villages, many of which aren't on the "must-see-tourist-desitination" radar and are as charming, beautiful, and worthy of a visit as the big names.