Right down Osceola Parkway past Gaylord Palms is Country Inn & Suites Calypso Cay and the Amerisuites Calyso Cay. They both get good reviews. Also, the Radisson Resort Parkway (the name just changed to something else but I can't remember what) is close by. You can get deals on it usually on Mousesavers, and I think it might be a site sponsor here, too.
EDIT: I see that the Radisson has double beds, so that's out. The Comfort Suites Maingate East has queen beds. It's right behind Old Town and would be easy enough to get to/from WWoS by using the connector road by the Walgreens on 192 (connects 192 and Osceola Parkway). You cna usually get a good deal for this place on HotelMartUSA.com.