DH is going to run the Boston Marathon next week
Just checking that you know the Boston Marathon's next month (21st, I think?) Not next week. Good to be early, not sure that early!
Keep in mind that is school break week in Mass. The museums and stuff will be crowded. (Of course, half the state will have fled to WDW, lol, but still lots of people with free time.)
Adding on to what some others have suggested, the Freedom Trail is the best "budget" thing to do. It's a small amount to get into Paul Revere's House, donations to Old North Church (I think you may have had to pay a small amount to go into Old South. Last time we went, we were in a group so things had been settled in advance.) It's a good dose of Colonial History and VERY well marked (follow the red bricks in the pavement). I haven't ever been on Patriots Day (been to the Sox game that day, but not FT) but I'd imagine they would have special events around that as well. (Lexington and Concord- right outside Boston, would surely have something going on.)
USS Constitution would be a must see (free). That's my DS's favorite part of Boston (lucked out he and I got to go on a turn-around cruise on it one fourth- whoo hoo!) They have a little museum there as well.
Bunker Hill Monument is right near The Constitution as well. The "mini Washington Monument", as my kids call it. Warning though there is no elevator if that's an issue.
I saw someone post about the ferry to Charlestown (were the Constitution is)- we always just walked it. Depends how budget you want to be
The trail ends (or begins, depending how you go) at Boston Common. Right next to that is the Public Garden. They have swan boats there that we try to ride every year. (It's just a couple dollars.) If your boys ever read Make Way for Ducklings, this is where Mr and Mrs Mallard lived. There are even statues of Mrs and the ducklings (Jack, Kack, Lack, Mack, Nack, Ouack, Pack and Quack!) (And my 11 year old still has to run ahead to take a seat on the ducks
.
We always have to hit FAO Schwarz as well. (Only budget if you can get in/out without spending money, lol.)
I don't think anyone mentioned the behind the scenes tours at Fenway Park. (around $10 I think?) Even if you're not big Sox fans, it's need to go behind the scenes/on the field of a MLB ball park!)
As said too, the trolley tours are fun. They pretty much follow the Freedom Trail (including the Const, I believe) You can get on/off and you get a fun narration (we do the Old Towne Trolleys.) Depends on your budget and how much walkers your guys are. The narration is nice (if you walk it, pick up a book explaining the sites. I got mine at the Bunker Hill Museum. I'm sure they have them at Faneuil Hall and Old South at least too.
We love the Duck Tours. They aren't cheap though and I'd get a reservation. They only go into the river (eg not the harbor), so I wouldn't think it would be too wavy, but we dont' have issues with that either. When DS was little, he got to "drive" it down the Charles. Not sure if they still do that or not.
As said, there is the aquarium, Museum of Science and Children's Museum. Nothing budget about any of those, lol (though if you have a passport membership from another science or children's museum, you can get into MoS or CM free.) Out of the 3, our choice would be MoS for your ages.
The T (subway system) is a great way to get around (don't drive- esp on Patriot's Day!!)