There are several "local" tracks in New Hampshire you can take your boy to. White Mountain Motorsports in Woodstock on Route 3 - several of the area boys and families race there on Saturday night. True, short track racing at it's best!
http://www.whitemtnmotorsports.com/
There's also Canaan Speedway in Canaan
http://www.canaanspeedways.com/
and as listed above, Star Speedway and many others.
We perfer White Mountain because many of the drivers are friends from Laconia, Belmont, Gilford and other towns in the area.