Yaffa,
the Noda Beyehuda probably has in the order of 50,000 descendants by now. Only 1878 are listed on Geni. It has been over 230 years... So there probably really no way anyone can find this information for you, unless they have a LOT more information. You'll just have to try and find your grandfather's parents, keep on going from there. You might not need to trace all the way back as many of his descendants were famous in their own light. So connecting to the should be enough.
I also have a similar issue. Our family has a tradition that we come descend from the Noda Beyhuda through my great great grandmother Rachel Leah (Landau) Schimmel. She came from a town called Dubiecko, Poland. Her father Shlomo Halevi Landau lived in Dubiecko as well or in the area. He was a Beyoner Chusid. They called him Reb Shlomo Beyoner! Rachel Leah was born around 1878, making her father born sometime around 1850ish. Any information that anyone has that can help connect him would be very helpful.
Thanks,
Moshe