I hope all goes well with your mom. I'm going through the same thing with my MIL. Anyway, check out Brigantine, Avalon, Stone Harbor, Ocean City- all in NJ. I grew up in Brigantine, but spent a lot of time in all of the other areas. Brigantine was the hardest hit with Sandy, and so inventory with rentals may be limited, but the other islands are further South and not quite as hard hit. You can also look at Rehoboth or Lewes Delaware.
Not that I want to discourage you from renting at the Jersey Shore (putting money into the economy there will definitely help in rebuilding!), but any homes that were not damaged and that are renting will most likely have construction going on nearby. Usually, there is a law that prohibits non-emergency work (such as a leaking roof, or a hot-water heater dying) from mid-June through mid-September, but it has been lifted in order to give homeowners less restrictions on rebuilding. It would stink to spend a couple thousand dollars on a house and have the house next door being rebuilt with hammering, sawing, etc. Just something to think about.