The Vielle ville is the old medieval and historic heart of the city with arcaded streets lined with the inevitable souvenir shops, but there are some interesting shops selling clothes and local food.
However, don't go on Sunday morning/afternoon (after 1pm) when there is the market and tourists, vans and market traders clog the narrow cobbled Rue Ste Claire, but there are plenty of hidden alleyways and squares behind the castle and canals where the tourists don't go. Just loose yourself.
Annecy lines 28 miles north of Chambéry and 20 miles south of Geneva. It can easily by reached by TGV from Paris and Geneva, as it's on the direct line between Valence, Chambéry and Geneva
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