Just outside of the town of Clinton, directly west of Boston, is the former longest tunnel in Massachusetts that makes for a great walk. There is a ton of interesting graffiti to look at, some history to take in, and paths nearby so you can explore non-tunnel areas as well.
In the Edson Cemetary outside of Lowell, MA lies the grave of one of America's greatest writers: Jack Kerouac. Fans trek and adventure from all over the country (and world) to pay homage to the Duluoz legend and leave him all sorts of gifts just in case he wakes up. While it's commonly believed to be a faux pas (paws) to walk a dog in a cemetery, if you check the rules, are respectful, and keep your dog on a leash, there's no reason you shouldn't be able to honor one of our greatest adventurers with an adventurer of your own.
Boston actually boasts the oldest city park in the United States in Boston Common. It not only features two off-leash areas, but also has historical markers, public art, and even food vendors at certain times of the year, leaving more than enough to explore outside of getting some great exercise.