How would you spend two days in New york with...?

I want to my girlfriend to new york for two days as a graduation present. We're visiting her dad in West Babylon, but I'm not familiar with NY. I'm from vermont though. I dont want to go clubbing, I want to maybe hold her hand and just explore. But I want to make it seem I'm clueless, and I want it to be romantic. I have $3-400 to blow. Including for taxi's, but I'm by no means able to go for a shopping spree just yet. Im thinking, drive in early morning and eat dinner with her father. Spend the night in west babylon at my old friends. Than what? Drive in have lunch, explore what...? No museums please. Romance is ideal. :) Should I taxi into the city? Its probably not worth driving, I cant imagine alot of parking lots closer.. How much is a taxi like that? Mind you, Im from a place that walmart closes at 8, and you have to drive 15 miles to mcdonalds. (Yes. Its BS. but im moving to VA beach.) so try to excuse some of my lack of knowledge lol. I also hate heights. Empire state building? No thank you. I would cry in the elevator and during that long line.. haha. Best place for dinner with a ladie? She doesnt eat seafood and a steakhouse isnt, well her favorite. Maybe italian? Thank you all very much!