Basketball Hall of Fame is in Springfield, Massachusetts - where the sport was born.
With a one to two hour driving radius and the Massachusetts Turnpike at your disposal you could actually get to Boston in your travel window. Inbetween Springfield and Boston is Worcester, Massachusetts.
1. Higgin's Armory - the largest collection of armor in the Western Hemisphere
2. Worcester Art Museum - actually a shockingly good collection
3. New England Museum of Science - part science museum, part zoo, a central Masschusetts insititution - say hi to the polar bears
4. Old Sturbridge Village - south of Worcester in Sturbridge, Massachuestts. It recreates life in the 19th century. Wonderful experience.
5. Worcester Center Galleria Mall. Once upon a time this was your regular mall. Then came the real estate bust, and the mall went broke. Now it's a huge indoor outlet mall. You can get some incredible deals in there.
6. The Boynton - a Worcester eating institution that has been there for two or three generations. I believe it is on Pleasant Street if I remember my geography. Be sure to get a Boynton Bucket, and don't say anything bad about Massachusetts sport teams while there.
7. Just take a drive North on Route 122/122-A. Start in Holden, Massachusetts and head north to Rutland, Oakham, Barre, all the way up to Orange. Foliage will be gone by that time of the year but it is a beautiful drive and takes you through the heart of central Massachusetts. The town center in Barre is how you would picture a New England town center in your mind. Watch for speed traps in Rutland and the state police in Oakham. The highway on my last visit was in excellent condition. Lots of opportunities to explore, antique, dig around.
8. Sadly Spag's in Shrewsbury is no more, being gobbled up by Building 19. However the new owners claimed they would leave things as it was. It's not Wal-Mart, but it is an amazing shopping bizzare to say the least.
9. If you go into the center of Holden, Massachusetts where 122-A meets 31 there are a couple of very well maintained grave yards with headstones from the 1600's and up. An amazing walk through time. Some of it can be chilling, for example you may see a bunch of children buried over the period of a few weeks and can conclude that a disease must have swept through the area.
10. Mount Wachusett State Park. National Geographic has this park on their top 100 state parks in the country. Take Route 31 from Holden north and after 20 minutes or so follow the signs. Really good views if you can drive to the top. The road is not maintained once it starts snowing. Of course you could always climb the mountain the old fashioned way.
11. The No Name Dinner in Oxford, Massachusetts. I swear to God, on my father's grave, on the lives of my children, one of the absolute best breakfasts you will EVERY have in your life!
Go to Oxford, Massachusetts via Interstate 395 South. I'm 99% sure it is Exit 4. Head into the heart of Oxford, cross the train tracks and when you come to the traffic light at Cumerland Farms (a conveinience store chain that locals call Cumbies) take a left and find a place to park (there is plenty available along the street). The No Name Dinner is roughly diagonal from a newer CVS/Walgreens/Rite Aid - some big new drug store. It is called the No Name Dinner because there is no sign outside declaring it's location. Your nose and your eyes will find the old traditional diner car that has been built into and around it.
When you order at the No Name Diner make sure you don't say something like, "two eggs" etc. etc. etc. Just say eggs, how you wanted them cooked, your meat etc. You'll never, ever, ever be able to finish all the food and you won't believe the price. The hamburger steak and eggs breakfast is my favorite.
Some locals may call it Carl's Dinner or the Oxford Diner. Carl was the original cook, but he died more than a decade ago. His son carries on the tradition.
12. Finally if you check out the Avalance Adventure Finder on this site you can learn about a number of area parks, including the Blackstone River Corridor National Park area. Lots to see and do all around you.
Hope this helps!