I can relate. We took the kids to NYC in April and around 4:00 on a Friday we just wanted to find a place to get a cup of coffee and hot chocolate for the kids and sit down for a few minutes. We were at Times Square and it took several tries to find a Starbucks or any quick service place that had seating. All the time the meltdown clock was ticking.
DW lived in Manhattan for awhile and we used to go there all the time before kids. This was DS8 & DS6's first trip and what a change in how we "toured" the city. We also learned the all important lesson of knowing where the nearest bathroom was at all times and having the kids use them whenever there was one around.
BTW is there a family friendly place near the Natural History Mueseum? We went there on a Sunday Afternoon and wanted to get some desert and coffee afterwards and didn't find much right in that area. We took the subway back to mid town and hit a dinner there.