Un Deux Trois is fine, not stellar, but fine. Good for pre-theater dinners. They have a crepe menu which is pretty good too.

West Bank Cafe = wonderful!

http://www.westbankcafe.com/menu.html

If you want something similar to Carmine's try Tony's di Napoli. If you make a reservation now, you should be ok. By the way, you can't make a reservation for two at Carmine's, but it's almost certainly open. But there are literally hundreds of restaurants within a block or two of your hotel, so you need not be concerned or frantic. And you will have no trouble getting a reservation for the 11th if you do it today. Just look on OpenTable and see what's available at your preferred time. Filter the restaurants to include only the Times Square area.

If all else fails, Virgil's is definitely not gourmet, though I don't like it much. And you can always eat at Heartland Brewery, which is not my favorite place but which has good burgers.

We like Trattoria del Arte - but it may be too far north for you. Definitely much better Italian than Carmine's (which is basic red sauce - fuel). And they don't take resies for 2. If you go be careful ordering - the portions are often grotesquely large and it's easy to get way too much food and spend way too much.

Un Deux Trois is an old (very old) standby. the food is fine for a casuale place and they will get you out for a show if you tell them that's what you need.

Haven't been to 1-2-3 in a while but it was always good whenever I ate there. They were known for their profiteroles.

Just a few doors away from it is Dopo Teatro, which serves very good Italian food and is reasonably priced. They have a pre-theater prix fixe menu which is a great deal and well within your price range.

I really liked La Rivista on restaurant row at 313 West 46th Street. I'm not sure how far that is away from the Algonquin but you might want to check out their website.

Un Deux Trois is so near your hotel.And you don't have to go into Times Square to get there!

La Masseria

I checked out a couple of these - like Doppo Teatro and West Bank Cafe. Thanks!!

I don't remember how I found the West Bank Cafe, but I've returned several times and it is always good. Several Fodorites have gone and returned to share that it was one of the favorite choices in NYC. I ate there on Thanksgiving Day one year and was surprised to see how many locals/regulars were there. It's so close to the theater district that it could stay in business with just tourist traffic, I suppose. But that's not their core business - it's folks in the neighborhood or in the theater business. It was fun watching the extended families being greeted on Thanksgiving Day. It's true there are hundreds of restaurants surrounding your hotel that you could just wander into. I've done that, with random results. The West Bank is consistently good, with good food, good service and a nice space. It's my new favorite in the area. Sam's used to be for years, but it's gone now. I was surprised (because she rarely travels more than a few blocks from her home) that it's also a favorite of my friend who grew up in the UWS. I discovered that via Facebook when a TV show was filming outside. What I like best about it for a pre-theater dinner, is that it's just steps away from the theater but not IN the craziness of the crowds of the theater district. I've tried other restaurants up and down 8th and 9th but other than grabbing a quick slice of pizza, I'll be at the West Bank if I have a say in the restaurant choice. The have a nice prix fixe menu and a very nice wine flight to match the courses if you are interested.

Not sure if we'll see a show or not. Sun shows seem to start at 7, maybe 7:30 for some. That would make a rushed dinner. And we probably wont' know till we check out the TKTS booth Sun around lunchtime.

If you have a smartphone you can know at any time. I prefer buying using discounts from broadwaybox.com. You may pay 10% more than the TKTS booth, but you "save" the time. I'd rather spend my time in NYC seeing/doing things than waiting in line.

starrs, I was just reminded that my first introduction to West Bank Cafe came from the poster Bug'sWife here, who recently passed away with cancer. Lee and I met her there for lunch years ago and we were instantly hooked. Such a good restaurant, although I really miss their cabaret/open mike Friday nights there downstairs!

If you want to see a show on Sunday, you would do better to look for matinees. Very few Broadway shows operate on Sunday evening or Monday, so you're going to be strictly limited if you want to go in the evening. Go to the show THEN have dinner.

There is a 3PM Matinee of Nice Work if You Can Get It. I think we'll try for 1/2 price tix to that then I made reserv for 7 PM at Dopo Teatro. That timing should work pretty well.
I'll keep West Bank on my list for another time (or maybe lunch?)