Hospitals in South Jersey

Cooper Hospital in Camden is big, and it is a Level I Trauma hospital as well.
There's also Our Lady of Lourdes in Camden and Virtua as well. Virtua is a growing hospital group (hospitals in Camden County and Burlington County). Kennedy Memorial Hospitals (Stratford, Cherry Hill and Washington Township) are primarily community hospitals.

Underwood Memorial in Woodbury is another community hospital. And if you want a small community hospital, there's Elmer Hospital (in Elmer, where else?).

That's all I can think of right off the top of my head.

South Jersey Healthcare located in Vineland

Atomic Woman pretty much named the biggies. A quick google search would have sufficed as well.