Annecy is a town built on a river that is only 3.5 kilometers long. The Thiou drains the lake straight through the old town, which is why the canals are so clear and why Annecy gets called the Venice of the Alps. The counts of Geneva made the castle here their main residence in 1219. After the Reformation closed Geneva to its Catholic bishop, Annecy became his seat, and Francis de Sales ran the diocese from here in the early 1600s. The town joined France only in 1860, with the annexation of Savoy.
Three days is the right length because Annecy has two halves that need separate days. The old town is tiny and takes one day, with time left for the castle and a long dinner. The lake needs two: one for the west shore by bike and boat, one for the east-shore villages. The gorges and mountains are fourth-day extras.
Day one is the old town, from the Palais de l'Isle to the castle and the Pâquier at dusk. Day two is the west shore of the lake by bike and boat, as far as Duingt. Day three is the east shore: Talloires, Menthon-Saint-Bernard and its castle, and the basilica above town for sunset. Start on a Friday: the old-town market runs Tuesday, Friday and Sunday mornings, the Menthon castle opens only Friday to Sunday outside summer and school holidays, and the Sunday buses to the east shore are the thin ones, so day three works best as the last day. Our France page has the wider picture. Most visitors fly into Geneva, which we cover in 5 days in Geneva, and the high Alps sit behind Annecy in 5 days in Chamonix and 5 days in Megève.