If you're there for 9 days, sure, that'd be fine to rent a car and explore New England. It'd also give you a chance to visit a few of the top breweries in the country, particularly Tree House Brewing in Charlton, which is about an hour west of Boston. There's great breweries in/immediately around Boston of course (Trillium, Nightshift, Mystic, Lamplighter are probably my favorites, but there's like ... 15+ now), but Massachusetts has great breweries outside of Boston as well. If you're a big big connoisuer you should really make the trip to Tree House and then stop at a bar in Worcester called Armsby Abbey on the way back. Armsby has, probably, the best beer selection in the North East, with 4-6 dedicated taps from Hill Farmstead in gods country Vermont, and it's one of the only places outside of the brewery where you can get their beer (which, similar to treehouse, regularly tops the "100 best beers in the US/world" lists)... But they also have imports from De La Senne from Belgium on fucking draft, other breweries from around the US like TRVE in Denver, Fonta Flora in North Carolina, etc. The next best "crazy selection" bar in the Boston area is probably Row 34 in the Fort Point area of Boston. It's worth going to.
Normally I'd say don't rent a car, but if you're there for 9 days, then you should for a few days of your trip to get out. For places outside of Boston to visit, Newport Rhode Island is awesome, beautiful, historic, a great place to visit. Closer by Newbury Port, Mass is great. Further a bit Portland Maine is a wonderful city, especially if you like beer (Bissel Brothers, Foundation, Element, RIsing Tide, they're all good). Portsmouth New Hampshire is also charming. For Massachusetts fishing/coastal communities, Ipswich Mass is great, and you get that New England fishing community charm (as well as a couple of the best seafood restaurants in the US -- Woodman's of Essex and The Clambox. Woodman's is more "on the water New England seafood place," but I think that the Clambox is better... it's just like... on a state route 5mi from the ocean so not very scenic). Connecticut is slowly building up some great breweries too, but Connecticut is far and not convenient to get to from Boston ... THere's two big casinos on the East coast of Connecticut, as well as a pretty good brewery near there (I think it's Fox Farm Brewing), but unless you're into gambling or to see a show at the arena, it's not worth going to. And South Eastern Connecticut has literally nothing else to do. Providence is great but if your'e in Boston there's not a lot that Providence offers that Boston doesn't.
For nature-y things... New Hampshire's White Mountains are about 3 hours away, Vermont's Green Mountains are another 45mins from that. If you were looking to travel to the mountainous areas, Conway New Hampshire is a great mountain town to visit, and then you could drive 90mins east to Portland Maine, and then drive down from Portland back to Boston for the final leg of your trip. If you're looking to stay in Masschusetts and do naturey things, Western Mass is really beautiful... There's a rural state highway called the Mohawk Trail, which is Route 2 out of Boston, and goes due west throughout the state into the Berkshire Mountains. Berkshires are very small compared to any mountain ranges on the West Coast, so just... don't be expecting real peaks, but's it's beautiful, and there's great breweries around small New England towns like Turners Falls, Gil, and then larger cities like Amherst and North Hampton. If you're interested in classical museum, the Boston Symphony Orchestra plays their summer series at an outdoor / covered venue called Tanglewood in Western Mass. It's an awesome amphitheatre, great experience. If you're going out that far, I'd recommend staying in a small town called Great Barrington.
If you're staying in Boston and not intending to leave to explore, don't rent a car. Driving and parking in Boston sucks, and you can take the T and Ubers/Lyft wherever much more conveniently. Boston is also a small, condensed city and very walkable.
May - June you've got the Red Sox which is a lot of fun, and the NBA season will mostly be wrapped up especially because the Celtics are a dumpster this season. THere's weekend stuff to do every weekend in Boston. I think that Harpoon Brewery's annual Five Miler and Harpoon fest is ... late May / Early June. I used to do that every year, but not anymore, it's too young for me. IT's a lot of fun if you're 21 - 28 or so. I think Harpoon beer is shitty by today's standards, but their beerfests are still really fun.
Something I always recommend to tourists is to take a Duck Boat tour. It's super, super touristy, but honestly, I grew up outside of Boston and went on one like... 5+ years ago for the first time for a work outing/team builder, and honestly, had a blast. I learned a lot of things I never knew and the tours take you to a few spots of the city that you can't get to any other way, like going up the Charles and seeing a terrific view of the city that is unique to just that spot. Sure, the DUck Boats and Freedom Trail are touristy things that towny hipsters will scoff at, but if you're a tourist from out of state you should do them, that's what they're there for.
IF you need anymore brewery recommendations all over the state and NEw ENgland, I've got a lot of them.
Beer related things to skip: Sam Adams is boring and their beer sucks, so skip. THey don't even brew in Massachusetts, so what's the point. Harpoon has a good tour, your mileage may vary on their beer, but their tour is fun... and the area around HArpoon is now really built up, where as... 5, 10 years ago it was a barren shipping container island.
For art things... Museum of FIne Arts, Isabella Stewart Gardner Museum, and the Institute of Contemporary Art are all terrific museums. I love the Gardner museum because it's unlike any other museum I've been to, super weird, small, tiny rooms, and it's the site of the biggest art heist in world history... so, it's worth going to for the mystery.
