A source told RadarOnline.com: "They're keeping it very, very low key. He's not one for the limelight and fame and she likes that about him."
Scarlett, 27, and Nate were also spotted having a cozy dinner with three friends together at a restaurant in the city's Bowery Hotel.
Another source told the New York Post newspaper: "Scarlett was rubbing his back and kissing his neck.
"He was wearing a short- sleeve, V-neck T-shirt and had tattoos up his arm."
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Meanwhile, Scarlett and her ex-husband, Ryan Reynolds - who she split from in 2010 after two years of marriage - have put the home they used to share together in Los Angeles up for sale.
The $3.6 million, four-bedroomed house in the Los Feliz Hills area of the city is eco-friendly with solar panels, floor-to-ceiling windows in the kitchen, living room and den and a private garden and outdoor bath connected to the master suite.
The couple - who finalized their divorce in July 2010 - bought the property in 2008 for $2.9 million.