A great place to kayak is north of Moultonborough Bay past Clark's Landing. Even the area around the Graveyard is a good kayaking spot.
I had kayak the Winnipesaukee river from Paugus Bay to Franklin where it joins the Pemi and Swift River to form the Merrimac. That was a beautiful journey. Of course you will have to portage around a few dams, but it is worth it.
This summer I am planning on kayaking the Pemi. from Lincoln to N. Hampton.