Hi Scott,
We live 20 minutes from Alexandria Bay and can give you some info on camping in the Thousand Islands.
The best location for your time frame (1st week of October) would be Wellesley Island State Park. We stay there often even though it is close to home. The park has full hookups, paved sites and is open until October 9th. You would need to make a reservation on Reserve America:
https://newyorkstateparks.reserveamerica.com/welcome.do Rate is approx. $36/night plus $5 for out of state residents.
There are other parks but Wellesley is the flagship park in the entire NYS Park System.