Coney in the winter can be amazing.
While much of the honky tonk has calmed down, the beach is still beautiful. Time your visit right and you can watch the Polar Bears swim. And Coney Island, USA (home of the Freak Show, Museum, Mermaid Parade, etc.) is still having events (check their website at Welcome to ConeyIsland.com!
Depending on the regulations, you can surfcast or even try to get some Herring on a Sabiki rig off the pier (dress warmly). If there are any expert Coney surf rats out there, I would be interested in hearing your fishing advice.
And Nathans is open year round.