Cherrywood Kitchen: Menu, Interior, and its namesake sangria with the housemade foccacia Cherrywood Kitchen is a new restaurant that’s on Hudson Square or the far west part of SoHo on Spring Street. This restaurant has the potential to serve good food in a place that generally a food wasteland. The space is reflective of the restaurant’s name having cherry wood tables and finishes and have a cherry red wall toward the back of the dining space. Airy from the high ceilings. The restaurant is under the helm of Chef Chris Cheung’s who has apprenticed at Nobu and Jean Georges and..