The winter Olympics in Vancouver were the impetus for building a heavy rail subway line between downtown and the airport, so I wouldn't say they would fail to leave a rapid transit infrastructure legacy. If Boston built some kind of speed skating track in Lynn it could justify extending the Blue Line and claiming it would derive long-term benefit from the Olympics, for example.
I think the big issue for Boston and the winter Olympics though is that nowhere in New England has a sufficiently steep/high vertical drop, and definitely nowhere within two hours of the city. Even Quebec City has issues with this and it's far more nested in mountainous terrain than Boston is. I don't think you could host many Olympic events in the Blue Hills, if any.
Are these amounts consistent with the 800m vertical drop requirement for the Olympics? Killington looks like the best bet -- the longest drop in New England and closest to Boston that meets the requirement. But it's still three hours away (Vancouver-Whistler was two). A Burlington Winter Olympics might make more sense if New England ever wants to host.
Given the number of peaks in NY and the fact that Lake Placid has hosted twice I wonder if Albany could ever pull it off. It'd be a real shot in the arm for that place.
I did a little research on this, and the next 2 Winter Olympic hosts (Sochi and Pyeongyang) will have coastal and mountain clusters separated by 37 miles. The largest city involved in the Korean bid has a population of 250,000 while Sochi has a municipal population of 350,000.
There's 208,000 people in the Burlington area and 516,000 people in the Portland metro, so based on recent precedent Portland might have a shot if the USOC wasn't so unpopular right now. Since Logan would be the nearest major international airport in that case (other than Bangor, I guess), the Downeaster could see a boost from that, and maybe the N-S Rail Link if the Federal Government decides that New Yorkers should be taking the train up...
EDIT: ^ I think Denver gets the next shot for a US city, possibly the next shot for either Winter or Summer. It makes too much sense. I'm surprised Salt Lake got first crack, actually.
I don't understand what the Fall River and Providence links have to do with the Olympics, though.
EDIT: ^ I think Denver gets the next shot for a US city, possibly the next shot for either Winter or Summer. It makes too much sense. I'm surprised Salt Lake got first crack, actually.