If you wish to stay in Fonda, Friday night there are a variety of options.
You are welcome to camp at the Kateri Shrine, free of charge. Unfortunately the Long House is closed for repairs. A few beds available in the Retreat House, although it is unlikely you will have a private room.
You are welcome to camp. Bring a tent and spend the night on the Shrine's lovely grounds.
The closest motel to the Kateri Shrine is the Riverside Motel in Fultonville, NY about 3 miles away. Their number is 518.853.3314. Call for reservations and current prices.