Hidden historical places I shouldn't miss in Boston?

You may find Castle Island (Castle Island) interesting. This was the site of various-named forts between the Revolutionary and Civil Wars when the area was truly an island, before landfill connected it to the mainland. It's a nice outdoor diversion away from the touristy places where you can get a tour of the fort, and it has a great view of Boston Harbor.

The Freedom Trail will take you through most of the highlights. Spend some time in the North End- along with the Old North Church, this area is also the site of The Great Molasses Flood of 1919, the Brinks Robbery, and the Skinny House at 44 Hull Street. Also head to the Boston Public Library. It's got beautiful murals by John Singer Sargent, if you go all the way to the top floor. There are also usually some nice exhibits from their rare collections.

If you have the time and can rent a car, there are also a TON outside the city. If you like American History, visit the John Adams Building in Quincy (accessible by train.) I'm also a big fan of the Lexington-Concord area. Along with being the site of the first battle of the American Revolution, you can visit Walden Pond State Reservation which inspired Thoreau, and  The Orchard House which was home to Louisa May Alcott. 

Boston is 'built' of hundreds of small neighborhoods which were born in the early years of America and one of the best ways to see them is to use 'the T', public transit. Outside of downtown, the Green Line(s) is all above ground and riding any branch out-and-back gives you a chance to see what's along the route: I particularly like the B, C, and D lines, esp. if you like old neighborhoods. Not all of the places along these routes are historically 'important', but the areas are centuries old and generally look it. Follow the B line to Boston College, the C line to Coolidge Corner, or the D line out to Waban, MA (one of my favorites). These are street level trolleys and you'll really get a feel for Boston.

While the other subway lines are very convenient for getting around, you'll have "prairie dog" syndrome using them: You move around underground, but if you're not familiar with your destination, you have to pop-up to see what's at a particular stop.

The same goes for the MBTA commuter rail. Again, not off the beaten track,but you can visit places famous from the American Revolution (Lexington (Massachusetts) & Concord (Massachusetts) which can also be very much on the tourist trail but which are worth the trip anyway) and from the earliest days of European settlement (Salem (Massachusetts), Gloucester (Massachusetts), Providence, Plymouth).

I personally love Castle Island, which has an old fort used in WWI and WWII that offers free tours during the day. If you don't mind renting a car, you can also visit Walden Pond right outside of the city and see the old cabin that Ralph Waldo Emerson used to right in. Have fun!