I live in Virginia but travel to upstate NY to visit family every summer. There is a shoe store on Public Square called Avon Shoes. It's a family owned business, and you can tell. They have a great shoe selection for both adults and kids (stride rite, new balance, DocMarten's Birkenstocks, and others), reasonable prices, and an attentive, friendly staff. I make a special trip when I come to visit simply to buy my children's school shoes, rain boots, and snow boots. They will even order the shoes for you if they are not in stock and ship them to you!
When in Watertown, go down to Public Square and stop by - they'll help you find the perfect shoe for you!