This bar and restaurant is walking distance from the Oyster Point and The Molly Pitcher Inn. They are known for their delicious Italian cuisine, upscale pizza, and brewery on site! Weather-permitting, they have a nice outdoor patio you can eat/drink at too.
This is a cute waterfront park not far from the Oyster that is a great spot to go walking or relax on the benches-- weather permitting of course!
If you're looking for good coffee... look no further than this Jersey Shore classic- ROOK! Located on White St. about a 5 min drive from the Oyster.