Walking around the UMass campus is something you can't miss if it is your fist time to the area. You can stroll by the picturesque library, old chapel, and campus pond. You can also see the somewhat less picturesque Herter Hall and Thompson Hall where Anton and Jess spent many of their undergrad hours.
Northampton (aka NoHo) is a quirky town a 15min drive from Amherst. There are great shops, restaurants, and bars. We recommend Paul & Elizabeth's for their vegetarian menu and Northampton Brewery for great local beers.
Located about a 20min drive from Amherst is a beautiful butterfly conservatory. This unique tropical paradise in the middle of Western MA is home to over 4,000 species of butterflies.
If traveling with kids this is a great little museum to see some of the art from Eric Carle's famous picture books.