PLENTY of great steakhouses in NYC. My favorite right now is BLT steak (trendy and chic). Dylan Prime is another great one. Can't go wrong with Sparks (traditional) either. If you want to go really old school you can venture over to Brooklyn and try Peter Lugers. By far the most famous steak joint in New York. Be aware if you do, they only accept cash (and Peter Lugers credit card if you've got one) Tried Club A. Food is ok but has a weird cheesy vibe. Straight outta the 80's lounge singer upstairs and Samurai swords hanging from the ceiling downstairs What I imagine a gay S&M sex club would look like.
Would stay away from Ruth Chris, Morton's and Capital Grille. Good in other cities (Chicago per se) but not in NYC.
For romantic places apropos for an anniversary without reservations weeks in advance I would try, One if By Land Two if by Sea, Aureole, and River Cafe (Brooklyn) Good luck!