We spend some time in that area every year. Our favorites are:
1. Saco River Camping Area,1550 White Mountain Highway (Rt. 16), North Conway, NH 03860 Phone: (603) 356-3360, info@sacorivercampingarea.com, GPS: 44.020649,–71.118434
2. Eastern Slope Camping, 584 White Mountain Highway, Route 16, Conway NH 603-447-5092
Our favorite is Saco River Camping area but it fills up fast and reservations are recommended. During the summer it is almost impossible to drop by with no reservation and get a spot. They have a five night minimum but if you call they can normally fit you in for shorter stays.
Some of the sites in the middle row are set up so you are awning to awning with your neighbor. Great if you are travelling with someone but a little awkward if you are sharing a site with a stranger. Let them know what your preference is when you book.
Eastern Slope is a great alternative. Nice but a little tighter.
The auto route up the mountain is interesting and a bit of a thrill. Worth every penny. Try some of the local restaurants in the area, we haven't found a bad one yet!
Safe Travels