If you are looking for "must see, should not miss historical sites" then start with the Freedom Trail. I will grant that the Freedom Trail sites in isolation are not the most spectacular historical experiences in my life. Boston has done a pretty good job preserving some of the major historical sites like the Old North Church, but clearly you're still in the center of a huge modern city with glass skyscrapers and the like. For this reason, I think the Freedom Trail sometimes gets a bad reputation for being an overrated tourist trap. What I found fascinating about the Freedom Trail was experiencing the human scale of the events in the early Revolution. I had just assumed as a kid that all the events like the Boston Massacre, Tea Party, Bunker Hill, etc took place over some huge area the size of Cape Cod. In reality, it's about the size of some golf courses.
By contrast, I found Plymouth Rock the most utterly skippable thing I've ever gone out of my way to see. It's just a rock. It wasn't even the coolest rock I saw that day.
In terms of fun non-historical sites:
- Red Sox game is a must
- Downtown aquarium is really nice
- Harvard campus is a great walk
- Sam Adams Brewery tour is free