The study is designed to see if a course of injections containing the NY-ESO-1 protein (a tumor antigen, marker expressed by tumors); in combination with an immune stimulant (adjuvant) Montanide, with or without resiquimod (another adjuvant) is well tolerated and safe in patients with surgically resected Stage IIB, IIC, Stage III or Stage IV (AJCC criteria) melanoma, a tumor that expresses NY-ESO-1. In addition, this study is designed to see if the patient's body's defense (immune) system can be boosted (strengthened) by this vaccine and if the addition of resiquimod to the vaccine makes this more likely.