Ohhh Hamilton is very different from Boston and Amherst (I lived in the Pioneer Valley for a year). Hamilton's more on the quiet side, more quaint. Not as busy as Amherst or Northampton in terms of small towns.
Hamilton has about 3,500 residents so Gate kids actually double the population for 7 months of the year but it doesn't really feel like it. It feels more like about 500 living right within walking distance to the town.
Stores? Not much at all- a hardware store, a health food store, a drugstore, a few beauty salons, a supermarket (nearest Wegmans is 40 minutes away), and the bookstore. There's a chocolate shop (YUM). There's quite a few places to eat- one sushi place, 3-4 delis, 2 breakfast-y, 3 pizza places... a Mexican restuarant (owned by 3 Gate students). There's also the Hamilton Inn and Colgate Inn for upscale dining. There's other cute places down on Route 12B to Cazenovia.
Most people work in the area since many are farmers but for those in the town, either they work for Colgate or do work in town. Many will commute to Syracuse for big jobs (like law and stuff).
A lot of us get by without needing to go into Syracuse for big-city stuff. When we do go off-campus, often they're road-trips with a bunch of people. There's plenty to do (and not just professors dumping tons of work on us) and we enjoy our company so we stay around.
I think the community itself is close-knit but there's a pretty fine line between Colgate kids and the townspeople in terms of town-gown relations. The foilks can't stand a bunch of kids drinking at night and leaving a bunch of mess in the morning. But they do like us when we're not disturbing them (like really interacting one-on-one).
Performing arts only happen at Colgate but sometimes the local high school puts on a play too.
Hope that paints some kind of picture for you
TMP