Assuming that you're going to Smith? Typically the students eat at the dining hall, but State Street deli and market is going to be the closest place for you to get dorm snacks and light groceries! Walkable from campus.

If you need a real grocery haul, the Big Y in Northampton is a dang delight and is a bike ride away (there is a bike path running past it!) Stop & Shop in Northampton is a little closer of a bike ride but the produce section is somewhat disappointing tbh.

You'll probably be 99% set for food with the dining hall, but it's so worth it to get into town if you can (drag your floor mates along for some bonding!) Shelburne Falls and Haymarket in town are great cafes, there's some cute clothing stores, and if you take the B43 bus (free with your student ID, leaves from campus), you can get to the bigger mall the next town over if you need to do a target/trader joes run or pick up some winter gear.

Welcome to western mass! Best part of mass - don't tell the Bostonians 😉

EDITING TO ADD: can't believe I forgot about deals and steals!! It's a little overstock store in Northampton with close to expiration canned and dried foods. They have the best prices on most things for sure and have a weirdly good selection of gluten free or other specific diet stuff like Bob's red mill products. Also a weird amount of discount Dansko clogs. It's an experience.

If you've lived in Boston proper, no, Greenfield is not rough or scary. If you've mostly lived in the wealthier suburbs, then yes, it is more working class. AFAIK the crime is mostly drug related rather than violent crime. I've never felt unsafe anywhere in Greenfield or Turners tbh, and there's a fair bit of art and music going on there as well as down in Amherst/ Northampton and up in Brattleboro, and plenty of nature! It's also gentrifying quickly given the affordability.