Via AC Expressway
Take either the Ben Franklin or Walt Whitman Bridge to Route 676 South. Follow the signs for Route 42, Atlantic City. That turns into the Atlantic City Expressway. Stay on the AC Expressway until exit 7. Then take the Garden State Parkway south to Cape May. The GSP ends at Route 109 South and takes you right across the bridge into Cape May. Cross over Cape May Bridge onto Lafayette Street, Cape May. At the intersection, bear right onto County Route 606 (Sunset Boulevard), then left onto Lighthouse Avenue.
Via Route 55
Instead of the AC Expressway, you can take the Route 55 South exit on Route 42, and head south to Route 47. Route 47 South becomes Route 347 for a short distance than becomes Route 47 again. Stay on it, and it will take you to Rio Grande where you can head south on Route 9. When Route 9 merges with Highway 109 stay on Route 9 following the signs towards the Cape May - Lewis Ferry Terminal. Watch for signs for Highway 626 which takes you south across the Cape May Canal. Make a right at Sunset Blvd. (Highway 606) and follow the signs to the Park. This route will take longer, but it is more scenic.