A very nice restaurant in NYC is One if by Land, Two if by Sea...I think it is in the Village, but can't remember exactly. It is quite posh, but then so is a lot of good class dining in NYC. I have been there twice and not been disappointed.
Slightly less posh, but very nice is [
www.redeyegrill.com]
NYC is one of my favourite cities, I think the best thing is just to walk round and feel the vibe of the place, it's just so sparky. And you MUST have a diner breakfast, they are generally superb.