When you go, be sure to look at the back sides and stapled attachments of all wills and probate papers. We were in the Surrogate's Office in Malone a few years ago, and found the original US Naturalization certificates for my husband's ggf, Angenor Viau, and another Viau, attached to the backs of probate papers. There were many pages, and we almost missed seeing them.
And on the back of Genor's certificate were handwritten names of other family members, in pencil, and probably in his own handwriting...
We were delighted to photocopy them! [Still looking for fellow descendants and cousins listed in those wills & probate papers, though...]