There are some good answers here, I'll also add Aeronaut which can have jazz acts here and there. Also the swing dance scene is starting to recover and while unfortunately some of the old stalwart bands of the scene have packed it in, there is a new generation of really excellent young musicians getting involved and helping to put Boston back on the map.

Lastly, some jazz has moved into smaller less dedicated spaces (including house shows), so it can be harder to get to where the players are. Your best bet is: next time you see a jazz show you like, ask the band leader or especially any side player you like where they are playing soon, and you'll get some great intel. Half of the time they'll say something you can barely google or sounds made up like "The Art Dungeon, in the basement of Papa Gino's" or whatever. Then you'll start to get a sense of where you can see shows and get closer to players and the music they're making. Go to Lilypad and triple the suggested Venmo minimum at the door and make someone's night, they'll tell you what they're most excited about coming up and now you've got a killer spot in your pocket from a musician who has the best energy you could ever hope for. Shit, like a quarter of folks playing around town are still in school so maybe you'll even get a "you should come to my senior recital at the shitty little stage in the old Berklee building on a Wednesday at 2pm" and it will be one of the best shows you've seen in your entire life.