Lunch tomorrow around 5th and 45th?
Inside the Pan Am Building is Naples 45 at 45th Street and Vanderbilt. They sell their pizza by the slice. And underneath Grand Central is a food cort.
For more upscale, go to Ammos on Vanderbilt and 45th. Great (upscale...not authentic) Greek. Thier grilled cheese sahndwich with fries is great.
Branzini, on the corner of Madison & 41st St., is a casual trattoria-style restaurant that serves Italian/Mediterranean cuisine. The menu includes things like salads and paninis, as well as more substantial fare. It's been quite a while since we had lunch there, but their version of the eponymous fish is one of the best I've had. They are open throughout the afternoon.