This is killing me so I gotta jump in :) Anywhere you go in NY will be Paleo friendly. A menu will totally state if you can't make any substitutions, so tell your friend to just run amok and have a blast.
If you can give me: actual location: LES, the Village, etc, price range, what they won't eat, what they would be interested in eating, then I can give you an absolute load of options. Below is something I posted on another thread for someone who was coming to NY.. they could be a start for your friend but are sprawled out. Cheers!
Food: I chose multi-tasking locations: Takashi - I had to review this place and.. woah. Offal and meat city. China Town - explore! Look for big letters on the windows that will be A B C, etc. Those are our new health rating system. The ratings don't scare me, if the food is good then I'm going, but probably stick to A or B, Xi'an Famous Foods - do not miss it. Wander around and you'll find great galleries and oddities. Korea Town - Explore but my favourite for Korean BBQ is BCD Tofu House - the kimchi is tasty cakes and you will get loads of banchan. Baby Cakes Bakery - Vegan, gluten-free, organic - if either of you have a sweet tooth, best in the city and will blow you away. The location is the LES, lower East Side, and good things to explore down there. Galleries, Essex Street Market, etc. Saxelby Cheese is located in that space as is Shopsins - tell Anne at Saxelby I said hello :) Eataly - touristy but worth it, you can eat and shop, and it's in the Flatiron District - good things to check out as well as having Shake Shack down the street for a Shack-Cago dog, bonus as it's topped with pickles made for Shake Shake from a Brooklyn company. Tehuitzingo in Hells Kitchen. It's a Mexican grocery but insane tacos in the back. You want a pig ear taco? You got it. You can ask to not have with tortillas but don't ask to pay less money.