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Atlantic City Country Club is right at that hour time limit you have. I remember that from the Coast Guard Training Center to A-City was like 48 miles, so, if ACCC is not within 1 hour, its not more than 90 minutes.
Logistically Wildwood CC is your best/closest course to Cape May. Historically they are open to a phone call in the shoulder season if you are a member of a private club. Similar to ACCC and Galloway they sit on the marsh/bay overlooking the town (Wildwood). It is Stiles and Van Kleek with changes over the years and Mike Cirba has stated that someone else was the original designer.