Depending on your location, and how willing you are to wait, you should check out: 

Sons of Essex

Crooked Knife 

Jane Restaurant

Penelope 

Hundred Acres

Five Leaves in Greenpoint is fantastic, probably my favorite.

Penelope(good but long queue) Peels (not amazing food but cute resto with great ambience) Sarabeth's Restaurant (the one near Central Park is my favorite) Clinton Bakery Café(their pancakes are too die for!) Cafe Orlin (nothing fancy just good eats) and Prune (there's ALWAYS a long queue here too)

I really like Jeanne & Gaston. They have really nice patio seating that allows you to get away from the traffic and noise. The food is amazing. They have an eggs benedict that is better than any I've tried. 

The location is great too if you want to walk around. Close to Chelsea, West Village, HighLine and Meat Packing District. 

Check out Bubby's in Tribeca - they are fabulous and everything is amazing. (plan for a long wait.) Locanda Verde nearby also has a delicious brunch (and dinner and everything else :) Those are my time tested favorites. I also just went to Root & Bone this weekend and absolutely loved it. None of these places take reservations so you'll have to wait, but it's worth it. Enjoy!

Sunday brunch has to be at Jane Restaurant. That's the only day they serve their house made granola, which is ridiculously delicious. Their French Toast is phenomenal as well, as is almost everything they make. 

Regular weekday breakfast has to be at Clinton Street Baking Co.. The wait is much shorter on weekdays but with the same menu. Their pancakes are incredible. 

I would say both are great choices for a young couple. Also, if you need a few more food and to do recommendations for the city, I've published an entire list here: http://eatwritewalk.com/2013/09/26/new-york-i-love-you/

Maimonide of Brooklyn (aka M.O.B.) in Boerum Hill if you like vegan, clean food. 

Some of my favorites:

Lafayette (Lafayette). Get fruit salad and some pastries.

Freeman's (Freeman's), located down a small alley.

Maialino (Maialino).

Make reservations soon!

Go to Norma's (at the Parker Meridian Hotel in Midtown) if you want outstanding food alserved in a trendy "scene". It is pricey by any measure but a real NYC experience.

There are a number of great places to "drunk brunch" which seems to be the hot ticket with the young crowds (ie: you can get bottomless mimosas and bloody marys).

Reference this Buzzfeed article instead of listing em all out here, but based on where you're staying there's likely one or many nearby:

http://www.buzzfeed.com/ariellecalderon/affordable-bottomless-boozy-brunches-in-nyc

Calle Ocho Harry's Cafe and Steak Crooked Knife

Try a hands on 'The Kati Roll Company' a perfect brunch on 39th St.

Cafe Amrita 

Three different locations for The Smith for Sunday brunch