If you're in Alton Bay you are fortunate to live near one of the best ATV clubs in NH.
http://www.newdurhamvalleyatvclub.com/ 
They have taken up where the Belmont Family Adventurers left off.
They have safety training classes for new riders and a wonderful (legal) trail system.
You didn't say how old your son is but keep in mind that ATV's are not "motorized babysitters". Definately join a club and plan on participating yourself.
As far as riding in Mass goes, there is a very small (5 mile) trail in Georgetown / Rowley State Forest. The only other legal trails in Mass are in the Berkshires. For more info on riding in Mass you can reach me at
[email protected]