Hmmm...your requirements eliminate every single Vermont state park since hookups are not available in any of them. That's too bad, in my opinion, as some of them are in beautiful areas.
Here are the two that I've stayed at that meet your requirements. This is not an exhaustive list, nor are these necessarily the best in the state, just what I have personal experience with:
The City of Burlington operates a campground at North Beach. There's no pool there, but a very nice beach where you can swim in Lake Champlain, and it's an easy jaunt to downtown Burlington. The campground itself is perfectly acceptable but not exceptional in my opinion.
Apple Island Resort in South Hero is pretty nice. The (free when its open, even if you don't stay there) tool museum is kind of interesting, too; a quite large collection of antique hand tools.