This is an older apartment (in a 100+ year old house), but it's in good repair. All the rooms have air conditioners. Basically, you'll notice the age in the bathrooms (small) and kitchen (which is kind of quaint). I lived in Cambridge, MA for 5 yrs, and it is essentially like any number of grad student apts in Cambridge. Sandra the owner is really nice, and my kids loved playing with her daughter (they were both there on the turnover days).
As far as location and Cape May go, you can definitely park your car and not use it the rest of the time you are there, except for maybe a grocery run on the first day or day trips. Lots of great restaurants to choose from, and the beach is close. Also, for those unfamiliar, the parking is tight on weekends due to day trippers, but during the week street parking is quite reasonable near the apt. And of course there is one space to use.