What's the best restaurant possible for next Friday night, or Saturday lunch?
I assume you want somewhere that you can just drop in and dine sans reservation. Did you bring / will you bring a jacket with you?
Very few restaurants do not serve any food at their bar/waiting areas -- Bouley, La Grenouille, Le Cirque, Four Seasons, there may be a few more I'm missing. But it's not that long a list.
Momofuku Ko, Blanca, and Brooklyn Fare don't take walk ins, but they are the exception, not the rule...you should of course check all their web sites for last minute cancellations.
Also note that some restaurants won't put a table for 1 on OpenTable so you might want to call just to make sure. And also ask to be put on a waitlist.
So essentially, most of the city is in play... unless you have other criteria.
If you are interested in the 3 or 4 NYT star type restaurants:
Le Bernardin serves the full prix fixe and tasting at their bar & the lounge tables.
Daniel also serves the full prix fixe and tasting in their lounge. You can reserve on OpenTable.
Del Posto serves the prix fixe menu but not the tasting menu at the bar last I heard (you could call and ask). I think they also offer a la carte at the bar.
EMP and Per Se only serve a la carte at their respective bars and salons, not the tasting menus (they don't do a 3-4 course prix fixe at all).
Jean Georges does not really have a bar; the bar is inside of Nougatine. But if you ask, you can get the JG menu at Nougatine's bar (prix fixe or tasting).
Jackets are required for dinner at Per Se, Jean Georges (but not Nougatine), Le Bernardin (but not in the lounge), and Daniel.
Jackets are preferred but not required at Del Posto and Eleven Madison Park.
Some bar areas, like the Nougatine at Jean Georges, Bar Room at the Modern, and Tavern Room at Gramercy Tavern, have a different menu than their respective formal dining rooms.
Also the bar at WD-50 is also the only place you can order a la carte. Bar diners can order either of the tasting menus or any two courses for $25; additional courses can be added at $15 per course from either menu.
Nearly all of Mario Batali's restaurants have bar dining and walk in tables. Babbo, perhaps? You can also dine solo at the bar at Scarpetta, Osteria Morini, or Locanda Verde.
April Bloomfield's restaurants are typically bar dining friendly (Spotted Pig, Breslin, John Dory Oyster Bar, and the newest--Salvation Taco), if you're willing to wait for a seat to open up. Bloomfield's typically spots don't take reservations for small parties at all.
Danny Meyer's restaurants also are walk in friendly. Bar Room at the Modern (mentioned above) or Maialino's front room, the bar and lounge area.
Same for Gabe Stulman's places: Joseph Leonard, Jeffrey's Grocery, Fedora (Au Pied de Cochon alum, whose cooking I think is a bit underrated), Chez Sardine (despite the name it is an untraditional Japanese izakaya), Montmartre (ex-Momofuku chef), and Perla (ex-Babbo chef).
You could also have a great meal at the bar/counter at Momofuku Ssam, Empellon Cocina, Louro, Pearl & Ash, Acme.
For a solo diner, you could try walking in with no reservation and sitting at the bar (bar room) where you can still get the full dinner menu. Old school classics that don't disappoint: Le Bernadin, Daniel, Babbo. Contemporary "classic" choices: Lafayette, ABC Kitchen, Gordon Ramsey at The London NYC. Enjoy!
On such a short notice it won't be easy...
Friday night all the top tier restaurants are already fully booked.
There is some availability at bouley on saturday at 12, or jean georges at 215, but other then those two I can't see anything else..
You may be lucky and score a last minute reservation at EMP or Per Se if there are some cancellations during the week.
Or you can go at the EMP/Per Se salon (walk in only), or the Le Bernardin salon (again walk in only and they serve their full menu as well).