@Morgan Oooh, absolutely!
Peter Luger in Brooklyn is the ultimate NY steakhouse. It's cash only and you need to make a reservation weeks in advance, but give them a call and see!
Keen's is the second oldest steakhouse in NY - loads of history and has a collection of 50,000 smoking pipes, including a few belonging to the rich and powerful. Interesting for history alone.
If you want trendy - look at STK meatpacking or Strip House. STK is a bit of a guilty pleasure of mine, because it's so pretentious, but the food is delicious.
I love to go to Porterhouse in the Time Warner Center. Grab a drink at Center Bar first and watch the sun set over Columbus Circle and Central Park. Or you could go and get a pre-drink at the very secret, very special hidden bar "The Office" in the Mandarin Oriental.
OR if you want to go rogue - M.Wells in Long Island City is over the river from Manhattan in Queens, but Michelin starred without breaking the bank. Always has interesting non-steak-y stuff on the menu. I celebrated a few anniversaries and birthdays here, and used to live around the corner.
Hope that helps! Happy to answer follow-up questions.