Tons of stuff to do. I've lived here for years so message me if you have additional questions.
The USS Constitution (Old Ironsides) will be heading in for dry dock soon but it's still open just a few days a week (Thurs-Sun). It's in Charlestown which is across the river from Boston. You can do the Bunker Hill monument while you are there.
The Freedom Trail in Boston is a link to many historic sites. It's quite literally a painted stripe down sidewalks & across streets. You can get a guide on line and then walk any or all of it. Paul Revere's house is on the route, as is Fanueil Hall which has a museum in it. There's a colonial burial ground, a couple of churches, and more. You can start in the middle of it if you want to - you don't have to do the whole length, and you don't have to stop in every location. Next to Fanueil Hall is a refurbished warehouse area called Quincy Market - there are 3 sections with a lot of shops and little kiosks but the center section has a pretty neat food court (real food, not just like the stuff in every American mall). Everyone can get what they want and then eat in the open area. There are also restaurants for sit-down table service. Nearby is the Union Oyster House which is a colonial-times restaurant - uneven floors and all! Seafood and clam chowder are outstanding here and in most other Boston restaurants.
When you get to Paul Revere's house, you're close to some terrific restaurants in the historic North End, which is the old Italian section of the city.
The Tea Party site is, obviously, on the waterfront and the Children's Museum is nearby. You don't say how old your kids are, but that's a good and interactive museum.
The Museum of Science is outstanding. So is the New England Aquarium. But both take good chunks of time. If you have a museum membership where you are, there may be reciprocal admission to other museums. The Art Museum is fabulous but, again, it's a half day's commitment easily. I would check each one on line to see if the exhibits (permanent and visiting) of all of these line up with your home school curriculum. The MOS also has an IMAX theater with fabulous films if those are relevant to you. The intro is narrated by Boston native Leonard Nimoy (Mr. Spock).
Do not try to drive through the city. Use mass transit, called the MBTA or "the T" - the lines are color-coded (orange, green, blue, red) and easy to navigate, with lots of places where they cross and you can switch lines. Most of the major attractions are on these lines. Or you can take cabs or use Uber.
Remember that winter in Boston is iffy. Some sections are really old so the cobblestones and winding streets can make plowing difficult and walking challenging. It's on the water, which sometimes means temps are a little milder than inland, but it also means there's plenty of wind and sometimes fog. So consider the weather when you look at walking tours, waterfront activities, or even going up in the Prudential Tower for a scenic view of the whole city. If you get a mild day, you can cross the Boston Common and the Public Garden, although obviously not much is growing now! If your kids are young and/or fans of "Make Way for Ducklings", re-read the story and then visit the site where the story took place - and there are statues of Mrs. Mallard and the ducklings. Kids climb on them and it's a fun place to take pictures. There are tourist trolleys that go through some of the streets with a narrator, and they do have covered sides if the weather is cold but not miserably rainy.
The John F. Kennedy Museum is south of Boston but accessible by mass transit. It's an outstanding place to visit to discuss not only his presidency but the cold war, the Cuban Missile Crisis, and the Nixon/Kennedy debate (first televised presidential debate and still heralded as a real debate vs. a bunch of sound bites with 10 candidates up there!).
Cambridge is across the river as well, and there is a Museum of Natural History near Harvard that's small and doable in a few hours - great geology exhibit (geodes, crystals), fossils, and a whole wildlife exhibit with neat specimens. There are some cute restaurants and some funky neighbors & shops in some of the squares.
If you venture north to Salem, it's a very pretty town and tourist-friendly. You can learn about the witch trials and visit the Peabody Essex Museum which is fantastic. This is a bit of a hike so you might want to stay in the city itself if you only have a few days to try to cover a lot of history!
Otherwise there are tons of ethnic neighborhoods and restaurants, and overall Boston is a very small city in terms of square mileage. Choose well, get a really good map (don't just rely on GPS), and work your way around in a reasonable fashion.
Wild Woman mentioned "Cheers" - we used to go there for years before the TV show, and it doesn't look exactly like the bar did in the show, but it's fun. It's also crowded. It's at the edge of the Public Garden.
Newbury Street is eclectic shops and some expensive shopping but it's cute. It has a lot of little restaurants.
Not sure where you are staying, but it's cheaper outside of the city but then you have to deal with a car and parking fees which can range from manageable to exorbitant.
As you start to narrow down your choices, feel free to message me for clarification or more info. Obviously I haven't listed everything here, so if you have other preferences, that doesn't mean they are bad ideas!!!