We have just become a certified botanical sanctuary and are opening our gardens (over 250 types of herbs) to the public on June 30th. We are located in Schoharie County, less than an hour from Albany. Let me know if this interests you and I will email you more info.

There are about a gazillion between NYC and Albany. I'd recommend starting with Wave Hill, and work your way north. The don't miss ones would probably be Kykuit, Stonecrop and Innisfree. Most of the house museums have some sort of formal garden. However, with several of them, the most extreme being Olana, the point isn't gardening so much as landscaping.

Albany and RensselaerCounty Cornell Cooperative Extension both have Demonstration gardens with themes such as grass, fragrance ,prairie butterfly etc.
The Rensselaer County garden tour is July 12, 4-8pm .St Henry's in Averill Park has one June 19th at 4pm -8pm.
The Soroptomist club in Schenectady is also having one June 16 10 -4pm . And heres a link to the Garden Conservancy
http://www.gardenconservancy.org/opendays/
Enjoy, Kareen