I've lived in and outside of Boston for years. First of all, it's a small city - so you can get from one section to another very easily. It's just not NYC or LA or Chicago in terms of mileage. You can also message Lori H. - she just brought her family here last year and I gave her a ton of info, but I honestly forget where she stayed. Use AAA or Groupon or the Hotwire type sites for current deals. The area you're talking about is prime real estate - but you can be in Brookline or Cambridge or Charlestown which are so incredibly close you wouldn't believe it.
The Freedom Trail covers a big expanse, and you can pick it up and leave it whenever you want. Faneuil Hall has a small museum, and adjacent to it is Quincy Market. You can walk to the waterfront from there, and you can get a good walk to the North End (the old Italian section) and Paul Revere's house as well as the Old North Church ("one if by land, two if by sea").
If you are coming in mild weather, you can do the Duck Boats which pick up 2 locations in the city, the Museum of Science and the Prudential Center. The MOS is fantastic (are you bringing your kids? it's great for all ages!) and a site unto itself. For history, you can also do the Bunker Hill area and the Tea Party ship too. Additional museums include the Museum of Fine Arts, the Aquarium, the Kennedy Library, and the Peabody Museum (natural history, geology, more) in Cambridge near Harvard.
Boston has a color-coded subway/mass transit system (subways downtown, trolleys on the outskirts, but you don't change cars in a color system). You can get a good map in a million places, but once you read green, blue, red, or orange, you can make your way easily, and there are places where they intersect. Several lines cross, for example, by the Boston Common and the Public Garden. These are great in good weather.
How long will you be here? Do you have any specific things you want/need to do?
Feel free to message me. I did a whole bunch and back-and-forth stuff with Lori, and she and her kids had a great time. Happy to help.