Get a cab or Uber. Not far at all.
You can take the Silver line bus from the airport to the Amtrak train station / public transportation Dept., but its across the street from the harbor (Intercontinental hotel). So it's not really near the Revere to walk. However, you will have a cheaper Uber ride from there. Under $15 or even less I'm pretty sure.
Honestly, I would get on the train or bus to the hotel. Its cheaper and as far as travel time, youre not saving much anyway. I would take the blue line to Gov't Center, then take the Green to Boylston and walk about 5 min to hotel.
You will have to transfer a couple of times. From Logan, you will have to take a shuttle to the green line subway station. We got off on the Chinatown stop. I forget which station we got on at but just make sure you end up at the Chinatown stop
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