The Freedom Trail winds through historical Boston, taking you to the grave of Sam Adams and along the cobblestone streets of the North End. Visit the Make Way for Ducklings statues in the Common or ride a swan boat in the Public Gardens. Get some Italian food and a canoli from Mike's Pastries in the North End. See the USS Constitution in the Navy Shipyards of Charleston. If you have limited time to sightsee, this will hit a lot of the highlights.
Boston is full of museums, and there's one for everyone. The Museum of Fine Arts has art exhibits from around the world and is located on the Green Line, The Museum of Science is world-class with constantly changing exhibits, the Aquarium in downtown has a resident population of penguins, and the Institute for Contemporary Art is in the Seaport District next to Harpoon. Boston Children's Museum and the Boston Tea Party ships are great for families in the Seaport as well.