You'd probably enjoy the National Silk Museum. With luck, they'll be running one of the looms.
The Du Jinsheng Silk Weaving Museum is also worth a visit. Much smaller than the National Museum, it's very attractively set in an old villa at the far reaches of West Lake. (Starting in the 1920s, Du Jinsheng pioneered modern weaving techniques in Hangzhou.) Allow time to explore this part of the West Lake precincts: beautiful, and not quite as crowded as the areas nearer the city.
I seem to recall that both of these places have gift shops.