The Discovery Museums are great, as you've already found. Also check out local libraries. I haven't been to the one in Acton (I live in Littleton), but Littleton, Ayer, and Westford all have nice libraries with children's rooms that have various benefits. The Acton library is on a different library system, but you can of course hang out at libraries even if you don't have a card. You can also attend library programs -- some are free, some are not. I don't know what is available through the Acton library, but check out story times and other activities through the Littleton and Westford libraries, and see what is available in Acton. Every town also has a playground, and I like to visit different ones to add some variety. My mom likes to take my kids to one in Acton with a duck pond (is that the one you found already?). Westford has several playgrounds near the Roudenbush Community Center -- during the day often one or more of them is in use by a preschool, but if no class is out there, you can use it (despite the sign saying you can't) until a class arrives. You can also walk to these playgrounds easily from the Westford library, and your walk takes you right past the fire department. The firefighters are always happy to give tours of the trucks. Littleton has a nice playground (Castle in the Trees) off of Rt. 110 (more or less across from the fire station). Also look into parents groups in Acton. I don't know of any, but it's likely there is one. Littleton has a very active parents group that arranges activities as well as facilitates playgroups. Also check out rec department programs through Acton-Boxborough and Littleton.
Another mom mentioned Perpetual Motion in Lowell. That is indeed a lot of fun, although a bit far for frequent visits. There's also One Stop Fun in Littleton. I like Perpetual Motion a lot better, but One Stop Fun is at least close by. Both are indoor play areas. You can bring your own food to Perpetual Motion but not to One Stop Fun.
Another thing to check out is local apple orchards. Many have additional activities besides apple picking. There is also the Ecotarium in Worcester, and much closer to you there is the Audubon Society's Drumlin Farm, which is excellent. There are lots of animals to see (it's a real working farm) and trails to hike. You might be able to get a discount pass through your library (and check out other passes, too -- many libraries have museum pass programs; I know Littleton and Westford both do).
Littleton is also having a town fair on the common this Saturday. There should be lots of kids' activities.
If you're looking for programs to sign your kids up for, The Little Gym in Littleton is great. It's less expensive than Gymboree in Acton, and the instructors are wonderful.
I hope this helps. Good luck settling in and with the baby! (I've got a 3-year-old and a 23-month-old and am expecting my third in October).