North Beach in Burlington is nice , its a bit urban,has a nice beach and is on the bike path. Burlington's a nice town. Button Bay is a VT State park further south and is right on the lake The NY side has a state park at Ausable Point thats real nice with canoe, kayak SUP rentals close by. There's also a SP at Crown Point just below the bridge to Vermont. Just above Plattsburgh NY is Cumberland Head State Park, convenient to town and a ferry to Vermont. There are some private RV Parks along the lake on both sides that usually book for the whole summer but it wouldn't surprise me if they had some transient openings. Lake Champlain is nice (I see it out my window every day), north of the Crown Point Bridge are the cleanest and deepest parts, south of the bridge it narrows quite a bit with more growth and weeds, although the bass fishing is the best down there. As for renting kayaks and canoes etc, my guess is that if you were close to either Burlington or Plattsburgh stores would bring boats to you. Ausable Point is real close to a spot where a kayak dealer sets up and rents all summer.
Let me know if I can help more.
Thought I'd add that you can bus into Burlington from North Beach which is 1.5-2 miles from town. Lakefront in Burlington is a happening place in the summer, almost always some kind of music or beer festival going on and a cool science museum as well (The Leahy Center). Burlington Boat house rents sailboats , kayaks etc. Just a short walk up the hill to downtown for food and people viewing.