This is a good stopping point, but there isn't much to do unless you bring a boat. Or you could use it as a base for exploring other areas in the Thousand Islands. It's only about 10 miles from Clayton.
We stayed here on a bicycle trip from Rochester to the Thousand Islands at the end of a 63 mile day. Don't let anyone tell you it's not a hilly trip coming up along Lake Ontario to the Thousand Islands! There will be hills! The good news is there are NY state parks along the way.
Burnham Point is a small (less than 50 sites) campground on the St. Lawrence River. It was a good stopping point after seeing the lighthouse in Cape Vincent on our way. There are sites by the river that are tent only but we pitched our tent up above. The tent sites were rather difficult to get to with our bikes. There wasn't much shade where we settled, but the sun was not intense as we arrived in the early evening and left the next morning. Unfortunately, I have no site photos and only have a photo of the sunset…but it's a beautiful view.
Restrooms/showers were clean, and there was electricity at the site. Unfortunately, the bugs were bad but that's just a summertime hazard in the Northeast.