Having traveled solo myself, happy to help.
Assuming you will be in midtown and don't want to spend time in sports bars, I would go for well-regarded restaurants with bar/tap room seating, both for the atmosphere and the food. Craftbar, Bar @ the Modern and Tamarind's Bar Room all come to mind, depending on the cuisine. If you like sushi and don't mind price, I tend to find Omakase a great solo experience as well (Gari in the mid range, Nobu at the high). If you are a guy looking to make friends and still have decent food/cocktails, try the bar at a place like Fig & Olive on a Friday or Saturday night. Also, in Chelsea near the high line is one of my favorite dining alone gems, Porteno (Argentine steakhouse) for the friendly food service at the bar and the solid selection of half-bottles of Malbec.
I just returned from 4 days in NYC, ate solo and every meal except one at the bar. Babbo and Momofuku Ssam bar both had great food, but were pretty crowded, even late at night. Aquagrill is great if you're a raw bar fan and it's very single-friendly. I also really enjoyed Acme - was treated very well, some of their dishes are designed to share but I had three small plates and left happy. Had a great long lunch at Del Posto and the food was great, but I found it to be relatively formal compared to the other places.
In the past I also had good luck at Red Cat, Otto and Gotham Bar & Grill.
I'll second everything Kathryn said - though I haven't been to Montmarte or Maysville yet.
Mission Chinese I like a lot, but I do find it's a little better with a group, since many dishes are served family-style.
Wong I'm mixed on - I like the boldness of his flavors, but I found a number of dishes to be a bit overpriced for the portion size. I've left hungry a couple times. That said... duck ice cream. Mmm...
Momofuku Ssam is fantastic for solo dining. I'd to stick to small plates and kind of make a "tasting" out of them were I dining solo, rather than go the usual app-entree-dessert route.
Another good place to do that is Morimoto, I find. Get a seat at the sushi bar - just don't bother ordering any sushi / sashimi. Theirs is serviceable, but it's just not a place you go to for sushi - really it's all about the creative composed dishes. There's good spacing between the seats at the bar as well, so you're not right on top of the next diner over.
- Salinas (great Spanish, both tapas and regular - one of the chefs from Txikito used to work for him at his old place, Meigas.
- Babbo (solo at the bar, if it's a weeknight, shouldn't be TOO long a wait - fun place to make a meal out of multiple antipasti, so you can try a number of things)
- WD-50, for something fancier - I find dining at the bar there very enjoyable, the bartenders (especially Jafrul) are good company for solo diners if they're not crazy busy.
- Marc Forgione - especially for his Chili Lobster, one of the better "Asian Fusion" dishes in town. (his famous Halibut "Proposal" also has Southeast Asian touches)
- Aamanns - mini Scandinavian open-face sandwiches, but elevated, super-fresh. Good for lunch or dinner.
- Xi'an Famous Foods (the Chinatown location has more seating than the one on St. Mark's)
Somehow I only typed half that sentence... weird. Updated to reflect: one of the chefs (Eder Montero) from Txikito got his start as Bollo's sous chef back in the day. Actually - and I'm not positive, so don't quote me on this - but I think both Montero & Rajj might have worked there, possibly where they met.
Almost every restaurant in NYC is solo diner friendly, especially if you are OK dining at the bar.
We have tons and tons of business travelers who drink and dine solo.
Do you have a budget in mind?
Where are you staying?
Do you prefer a table or grabbing a seat at the bar?
Any favorite cuisines? Favorite foods? What are you looking for?
Are you looking for beer, wine, cocktails?
Thanks for replying, I dont have a budget, Its more good vibe, and good food that will impress me. I like Asian fusion - Western take on Asian food. Staying in Chelsea but wiling to go to out of the way local places. I'm ok with the bar, think its a bit more interesting. Wines while I'm eating. Like your questions!
In Chelsea, my favorites include Txikito, Montmartre, Co aka Company. You may also enjoy Hanjan, Maysville, Eataly.
However, you might also want to do a restaurant doing creative takes on Asian, like at Momofuku Ssam Bar, Wong, Fatty Cue, RedFarm, Mission Chinese, Kin Shop, Danji, or Chez Sardine.
If you like good food, counter dining, a fun and boisterous vibe, and fusion-ish food, is definitely pick Momofuku Ssam for at least one meal.