Winonanick,
I suspect if you're looking at grad schools you'll be hitting areas like Syracuse, Albany, (maybe Plattsburgh?), Burlington, Hanover, Durham? In that case, you'll probably not want to have to drive too far to find your camping/hiking/canoeing spots, or you'll have no time for them.
I'd always suggest camping at the state parks. They don't have the packed-in RV setup that private campgrounds have. I've encountered a few exceptions, including Maple Hill Campsites in Bristol - about an hour south of Burlington - a really pretty, isolated campground within a very short drive of the trail up Mt. Ellen, which is a moderate, pretty hike, maybe 6-8 miles round trip (it's been a while since I did it, can't remember exactly). This campground is fairly close to Camel's Hump as well, which has a patch of alpine tundra at the top although it's often crowded on weekends - their website is
http://www.sover.net/~maplehil/
For moderate hikes not far from the main routes you'll be driving, here are a few:
I-87 north from Albany
Giant Mt. is 6 miles round trip, very steep 4,000-footer but really beautiful, maybe 15 minutes from the interstate, 2 hours north of Albany
Tongue Mt. Range - lots of options for short or long hikes; this ridge sticks out into Lake George from the northern end, maybe 1.5 hours from Albany
Rte. 4 between NY and NH
Pico/Killington near Rutland - you'll hike through some ski areas but the woods are quite pretty and the views are nice
Rte. 9 between NY and NH
The Long Trail/AT crosses here and although it doesn't go over any major peaks, there are a lot of pretty woods in this part of the state
I-89 from Lebanon to Concord
Mt. Kearsarge - easy hike for an afternoon or morning, big bald area on top of the peak, about a half hour NW of Concord
Mt. Sunapee - Lake Solitude a really pretty pond on the way up, ski area at the top with views, maybe 45? minutes NW of Concord
I-93 north of Concord
Mt. Cardigan is about a 6-mile round trip hike, big bald area on top with good views of the White Mts. - probably an hour from Concord, with the dirt roads - I could be wrong on the time estimate
Stinson Mt. in Plymouth, another good afternoon hike, about 4 miles round trip, views of the southern White Mts., 1 hour from Concord
Cannon Mt. or the Kinsman Mts. in Franconia Notch - both routes pass beautiful Lonesome Lake w/views of Franconia Ridge, views at the tops, only about 6 miles round trip for Cannon, a bit longer for the Kinsmans, 1.5 hours north of Concord
All kinds of other hikes in the Whites. I won't go into those - other people have done that.
Have a great trip