Friedman,s is a local chain known to have gluten free offerings (although Teh only mention on their menus is gluten free bread. (I thought they had other gf offerings). They have a location in your hotel. It's the one listed as “theater district.”
Here's a list of many other places but I don't know how up to date it is.
I was just getting ready to post the same question! I am celiac..arriving in 2 weeks so I will update you on my gluten free experience!
I have celiac!
Friedman's doesn't have a separate GF menu but nearly their entire menu is GF or can be made GF. They only mention bread on their menus because everything else most likely already GF. They're very knowledgeable about cross-contamination and very safe.
Also near Times Square I would recommend Nizza for Italian and Don Antonio for GF pizza. Also come up to the Upper West Side for Modern Bread & Bagel/Arba/Thyme & Tonic, which are all 100% GF and amazing.
Etcetera Etcetera has a full gluten-free menu.
If you are looking for only dedicated gluten-free food, Modern Bread/Arba is one of the best in the city.
You can also find lots of recommendations here: