From Huron you have direct access into Erie; No locks via the St Cair River, Lake St Clair and the Detroit River.
Once on Erie you have a few options.
1) Pick up the Erie Canal right in Buffalo New York which brings you to the Hudson just North of Albany.
2) Take the Welland Canal into Lake Ontario and pick up the Oswego Canal which will bring you to the Erie and the Hudson
Depending on how far North the boat is, you can also take the Trent Sevren water way in Northern Lake Huron and Georgian Bay. This will get you to Lake Ontario where you would once again pick up the Oswego Canal.
The Trent is a very scenic waterway but you will have to call ahead as there are many restrictions.
These are you most direct routes.
I don't recommend the Champlain system as this would take you out of your way.
You can also go the very long way and take the St. Lawrence out to the Atlantic.
New York State Canals: Maps