It depends on what time of year you'll be here. The Chocorua KOA in Tamworth is very nice as is the KOA in Twin Mountain. Depending on the size of your rig you may be able to get into a few of the Forest Service campgrounds which for the most part have no hookups but are in very scenic areas. Branch Brook Campground in Campton is one of my favs , it has huge sites and is fairly quiet but the infrastructure is a bit run down. The Ammonoosuc Campground in Twin Mountain is nice but a bit tight. The owners are very friendly. My favorite is The Baker River Campground in Rumney. Right on the river, owners friendly and helpful, quiet and easy in and out. There are a ton of CG's in the Whites, check RV Park reviews too http://rvparkreviews.com/
My husband and I just returned from a tour of the East Coast and stayed at the Pemi River Campground in Thornton, NH. You can read my review of the cg at the website listed in a previous post. We were very happy at this campground and the staff was friendly and accommodating. It was just off the interstate 93 but in the mountains, quiet, and accessible to many lakes & streams for fishing. It is a privately owned campground so no GS, C-t-C, etc. discounts; however, owner is a Vet and gave us 10% off due to husband's DAV status.