I just wanted to mention this little hike I did with the family because it's so close to Boston and it never seems to come up when discussing outdoor trips. I'm posting here because there's a campground associated with the mountains and they are very hammock friendly. This seems like a good hike and place to stay one of your kids to get them started in hiking and hammocking. And the big bonus is that it's about 90 minutes form Boston.
So we did a day trip to Pawtuckaway ... the New Hampshire state park is made up of three small mountains, North, Middle and South Pawtuckaway. To get there take 95N to 101W, then to 154. The state park is 1/2 a mile form the exit.
There's plenty of hiking and bouldering available around North Pawtuckaway, and the attached map shows those trails. On North Pawtuckaway there is a nice boulder field where people go to practice and an interesting area called the Devil's Den...a dark, dense old growth forest that's provides cool temperatures, caves and an incredible silence that's hard to find outdoors, certainly that close to a major city.
Back to Entry-level hiking with a hang for kids, consider South Pawtuckaway. South Pawtuckaway is accessible from inside Pawtuckaway State Park campground and the trail that leaves form inside the campgound is about a 6 mile round trip to the top. It's not a high peak but it's very open and provides great views - and that gives younger hikers something to work for. There's also an old fire tower and the climb up the rickety stairs improves the view even more.
After the day hike, get a spot at the campground and hang for the night. There's a nice beach and a small store as well. It's a big campground, but the best sites are the waterfront sites on Horse Island. I walked in with my son a few weeks ago and got site #3 that had just cancelled. It was a great site with hanging right at water's edge.