Market Cafe is fine, but nothing special. Sort of a high-end diner. I eat there if I'm seeing a show, but it's not a destination restaurant. For an even better version of this style of restaurant go to Alias (
Alias Restaurant | Fresh Friendly Neighborhood Dining).
The best bar food in town by far is The Spotted Pig (
The Spotted Pig - New York). Everything there is delicious. It's ridiculously crowded on weekends though. Lots of celebrities.
Another favorite is Momufuku Noodle Bar (
momofuku » Noodle Bar). The have a lot of counter seating so it's perfect for one person.
The most social restaurant I have ever been to in New York is Socarrat Paella Bar (
Socarrat Paella Bar). It's a tiny place with two communal tables and everyone talks to everyone else. They have great tapas. Unfortunately you can't get the paella because it only comes for two.
Gotham is great, but it's borderline fine dining, which doesn't seem to be what you're looking for.