My wife and I have tent camped for over 35 years both with our kids and alone. We spend the bulk of our camping time up on Maine but this year we're going to hit the southern VT areas a bit harder. We're going to be camping on the Battenkill in order to do some serious fly-fishing for a couple of days. We typically go further into the summer in September to avoid the crowds but I don't think it's going to be that crowded there. Also, any of the great state parks in VT are good bases for hikes or fishing especially Jamaica State Park. Right up off of Rt 9 right on the West River. Very nicely run and clean and quiet. Fishing there is always great, too.
If, however, you would like the ultimate in tent camping, head up to Lubec Maine and camp at Cobscook State Park right on the bay of Fundy. I can't explain how gorgeous it is there and how private and peaceful it is. I sat in a camp chair in the middle of the day and it was so quiet I could literally hear a pin drop. I even tested it. Check it out but it is a very long drive.
Rome
Allow me to also ad that for something really different, go to the Delaware Water Gap and camp right on the Delaware River. Really beautiful there, too.