As everybody else has said, make reservations early/soon, particularly for the weekends and doubly so if you're camping on July 4th weekend.
What sorts of things are you interested in? I get the general impression that rural/natural areas and activities may be higher on the list than cities and nightlife.
Consider spending a day or two in the White Mountains of New Hampshire; there's lots to see and do there, several very pretty drives, and many places to camp.
The Vermont state parks are lovely but don't have many camping amenities--typically, you get a picnic table and a fireplace/fire ring in the site, a simple but functional bathhouse (pay showers), a dump station, and central fresh water spigots. None have hookups in the sites. Many have rather limited site selections for larger RVs (but maybe not quite as limited as the web site listings sometimes suggest). Brighton State Park, in Island Pond, is one very nice park (on a little lake).
In the Burlington area, the city of Burlington has a campground at North Beach (with hookups). The beach is very nice, though popular during the day, and the bike path runs through the park (and extends for many miles). I've also stayed at Apple Island Resort, in South Hero (island), and was generally satisfied. They do have a neat antique tool museum there (mostly hand tools).
The Shelburne Museum is also worth a day or two to check out. It has an very eclectic collection, including hat boxes, a lightouse, a walking beam steamship, folk art, and a carousel.