You can definitely do this. My husband and I got married in Central Park as well. For our dinner, we went to a Spanish tapas place called La Nacional, located at 14th St. bet. 7th and 8th Ave (http://www.lanacionaltapas.com) We ordered paella, 3 different appetizers (as much as the table needed), sangria (again, as much as the table needed), and dessert for a price of $35. pp. We had 15 people. Ask for the front room, which faces the street. The back room is in the kitchen area. Good luck!