I second the recommendation for the Merrymeeting River, the put in is on the right of Route 11 just before the bridge that crosses the river. I have not paddled the upper part so I have not much to say on that section, but below Route 11, the river meanders through a marsh area and is nice flat quiet water with lots of potential for wildlife (depending on what you are looking for) and can easily be paddled back up stream if you are looking to avoid having two vehicles in the mix.
This is a great night paddle as well, pick a full moon night and enjoy the area, not a ton of trees around the marsh area and you can paddle to one end and back in a few hours.
McDudes small lake recommendations are also very good, nice quite water (no really large boats and lots of shoreline to explore)
Off 140 in Gilmanton, just below the Iron Works, turn onto Crystal Lake Road (big sign), Crystal lake is first and Manning is second, both on the right side of the road.
South of Silver Lake in Tilton down the Winnipesaukee River is also a nice paddle, take out is at the train station in Tilton.
http://www.americanwhitewater.org/co...mary_state_NH_ This is the list of all the rivers in NH that have a little bit of movement to them, class I and II can be handled with intermediate paddling ability, Knowledge of reading a river should be a skill that you have before attempting any class of whitewater. (Tongues and V's, know what they mean when you see them) If you do not know, then find out and practice. Plenty of books on the subject, and start slow with a small group and you will open yourself up to a far greater list of possible paddles in the area. Most small rivers in this area have some form of whitewater, but they only last a very short distance, so you get to enjoy the scenery on the rest of the paddle and have a little excitement mixed in from time to time, plus you can always portage if you are not comfy with the rip. Scout first until you can read from the boat and always scout a horizon line, even if you have run it before.