As mentioned above, it is a great area for exploring. Here’s one idea for a short walk.
From CSC, go one block north on Third Avenue, then turn left (west) on 14th Street and turn right on Irving Place. Irving is just six blocks long and is charming and interesting. You’ll pass the big high school across from Irving Plaza (the rock venue), There’s a Michelin starred tapas place at 16th and the (apocryphal) residence of Washington Irving across the street, At 18th, go in Pete’s Tavern, where O’Henry wrote “Gift of the Magi” (second booth on the right) and Ludwig Bemelmans drew a lot of Madeleines. Check the hundreds of photos on the walls. They won’t mind if you just tell them you want to look around.
Lots of pretty buildings with places to eat and drink. At the end of Irving (20th Street), you dead end at Gramercy Park, where a statue of Edwin Booth as Hamlet is facing you. (NB: If you turn left on 20th, the second awning is the entrance to the Players Club, still in operation today.)
I know you said you’ve already seen restaurant recommendations, but if you need more, let me know. (In the other direction from CSC at 10th Street and Second Avenue is Veselka, the longtime Ukrainian restaurant that is more popular than ever these days.)