I might suggest the Walpole Motel, a scant 1.5 miles away from Gillette Stadium - very walkable. Charming, homey feel, to this quaint New England Inn. Complete with itinerant non-English speaking commercial roofers, 8 to a room. Also features access to several purveyors of fine artisanal opioids and stimulants. Like the foliage, the methamphetamine and percocet is top notch in New England in the fall. If you book Walpole Motel on the right evening, you may also get to enjoy a local underage drinking/drugging party in the adjacent room. You can experience all New England charm for around $100 a night; weekly rates available.
In all truthfulness, getting to and from Gillette Stadium by car absolutely sucks - whether you're coming from California or 10 minutes away. It's enough to deter people from going to games - unless you can get there and be in line when the lots open and stay until the mounted state troopers kick you out. Boston or Providence, it's going to be a ****show - unless, as I said, you leave super, super early and stay 2+ hours after the game. PVD is definitely better than Logan. We just flew into PVD from the Caribbean (boy, my arms are tired). We always do green bc Boston sucks - this city itself is a ****ing dump, unless you like the smell of weed and homeless drug addicts on every third corner.
If you're thinking of a 1 pm game, which I think almost all home games are, and you're NOT taking the ****ty Pats train, I would leave your hotel by 7 am. Get to the stadium super early and grab breakfast at one of Krafty Bob's hotels in Patriots Place (not sure if anyone else in Patriot Place has breakfast, other than Dunkin Donuts - that is, if Krafty Bob lets you park in the retail lots before the game. That way you avoid the am traffic. But as others have said, Pats train from PVD may be the way to go. The last time we took the Pats train is ****ing sucked. Granted we took it North but the ride took well over an hour for what should literally be a 15-20 minute train ride.
Anyway, good luck