Bike camping like Santanoni

Is there anywhere in the park similar to the Camp Santanoni area where you can bike in a fair distance and camp overnight on designated sites?

We're already planning on staying at Santanoni for up to 3 nights, but may check out another spot on the last night if worthwhile. We're coming in from the Niagara-Buffalo-Syracuse I-90 corridor so ideally we don't want to venture too far north or east of Santanoni.

Thanks!