You'll LOVE Cape May. Do plenty of research before you go. You can be lazy and quiet or be busy but not with things like amusement parks/boardwalks and other high-energy stuff and there are a lot of "night club" type places as well.
I have stayed in 4 of the hotels in town...3 which are right across from the beach. There are a number of hotels on Beach Ave which is across the street from the beach. The majority of rooms at these hotels have a beach view if not a beach front view. There are no hotels "on" the beach.
I've stayed at Sea Crest which I see some folks recommending. It was quite some time ago though. We prefer efficiency units when we go and the Sea Crest efficiency unit we had was very nice. Nice sized living/dining/kitchen area with a sofa, table & chairs. Separate bedroom with 2 beds. Pool. Jacuzzi.
Some things to do that I highly recommend are visiting Cape May Point State Park, walk the wildlife trails. Sunset Beach for sunset and the flag lowering ceremony. Birding By Boat on the Osprey. Dolphin Watch Sunset Cruise aboard The Spirit of Cape May. Shop the Washington Street Mall--enough places to dine there you can eat somewhere different for every breakfast and dinner! Take the time to make the short drive (15 minutes approx.) to visit the Cape May County Zoo--it runs on donations so you can pay whatever you want to go in. They have an excellent breeding program with their snow leopards there, hopefully there will be a new cub/s again this spring.
I have reviewed several Cape May places if there is a way to click on my name and see them all, I'm not sure.
I also have a Facebook fan page for Cape May Point State Park:
This site may be of some help to you:
I'm confident you'll enjoy yourself.