Unfortunately I came up mostly empty on looking for camping between Albany and NYC.
I expected that some of the towns along the trail would be willing to let cyclists set up a tent in their local city parks - this is a common practice along other long-distance trails like the Katy Trail in MO and Cowboy Trail in NE where the trail towns welcome cyclists to overnight in city parks. However, after talking with the parks people and/or town hall people in about a dozen communities between Albany and NYC, every last one of them told me that cyclists are NOT allowed to set up a tent in the town parks.
There are two established campgrounds along this portion of the Empire State Trail, not on the trail but within a reasonable distance for cyclists - Sam Pryor Campground near New Paltz, and Sylvan Lake near Hopewell Junction. However, both sites require riding a few miles on county roads. The road to Pryor lacks a good shoulder about half the way.
I wrote up everything I could find on this web page: Camping Along the Empire State Trail
If anybody knows of, or discovers any other good camping options, please share the info. Lack of camping options will discourage many touring cyclists from using the Hudson Valley portion of the Empire State Trail.