Take New Jersey's Garden State Parkway South. The Parkway ends at Cape May. (The road turns into Route 109 South just before the Cape May bridge.) Drive across the bridge and you're on Lafayette Street.
Take I-95 North to the Delaware Memorial Bridge. Once across the bridge, you can take the first exit, that will put you on Route 49, or the next exit that will put you on Route 40. Either of these will take you to Route 55 South. Route 55 South ends at Route 47 South. Route 47 South becomes Route 347 for a short distance, then becomes Route 47 again. Follow Route 47 South to the Garden State Parkway South. The Garden State Parkway South will end at the entrance to Cape May; you will be on Lafayette Street. Follow the signs to the beaches, or the center of town.