There is the Northville-Placid Trail. From Lake Placid you could do the West Branch of the Ausable River, and down.
Then you could do a loop from Seventh Lake->Shallow Lake->Eighth Lake
The NCT is not completely mapped through the ADK's, but between Rome, NY and Boonville, There is the Mohawk River, Delta Lake->Mohawk River and up RT 46 along Lansing Kill. About a days hike will then put you on the Moose River or Black River.
Lots of water in the ADK's, I usually bring a rod up there.