There any number of great hikes of all lengths and difficulties, many close by and others within 1 to 1.5 hours travel time. It would help to have more information. What sort of trail length and elevation gain do you have in mind? How old and tall is the kid, and can he negotiate stream crossings that involve minor rock-hopping? Are you looking for a great view from the top or just a nice trail with some views along the way?
Of course there are the White Mountains, with the AMC's list of 48 4000 footers, involving 4-5 miles each way and up to 4000 feet of elevation gain, and many have difficult trails for a small kid. But there also are some easier ones. Perhaps the easiest is Mt. Hale, with an elevation gain of just around 2000 ft, and a trail length of 2.3 miles, but there is no particular view from the top, and there is one stream crossing involving rock hopping.
Then there is the "52 with a view" list (
http://4000footers.com/list_52wav.shtml). Fairly close on that list is Mt. Israel, over in Sandwich (
http://4000footers.com/israel.shtml), with a trail length of just 2 miles and a great view north and east. Another might Mt. Pemigewasset, up in Franconia Notch (
http://4000footers.com/pemigewasset.shtml), at 1.7 miles each way.
But give us more info as to what you want and what the kid can handle.