I recommend a minimum of 3 nights at Liberty Harbor, giving you time to make several trips into Manhattan. The NY waterway is very convenient. You will have more ferries from Paulus Hook if you are willing to walk about 1 mile. It's a fun way to get over the city and only costs around $8 each way.
http://www.nywaterway.com/PaulusHookTerminal.aspx
Wildwood is very commercialized. Sea Aisle City, Avalon, and Stone Harbor have much nicer beaches and boardwalks in my opinion, Wildwood makes a nice 1x visit. There are many campgrounds down in that area and they won't be cheap in July. Get to the beach early to beat the crowds and heat, then relax poolside in the afternoon. Beach tags are required on most public beaches, but very modest in cost. No dogs. Biking on the boardwalks is fun and limited to certain hours.