I am from Cape May. I am actually going down tonight when I get out of work today. Luckily I have several free places to stay with my family there.
Everyone is right, the closest airport is AC. Spirit Airlines flies into there. Cape May itself is pretty expensive but there are places on the next Island over, Wildwood Crest that are more resonable is is only 5 miles from Cape May( just over the bridge). The other option is to camp as there are a few campgrouds if you are into camping.
Some nice places in Cape May are: Congress Hall, La Mer hotel, Atlas Inn. If money is no option I would suggest the Southern Mansion. Make sure you eat dinner at Lucky Bones (Across from the Lobster House), its great.