If you only do one thing, you HAVE to get tickets for Sleep No More, an interactive theater experience that's actually best done solo.  For cocktails, check out Booker & Dax, Please Don't Tell (hidden behind a telephone booth in a hot dog shop in the East Village), and the classic Death + Company. I also love going to check out whoever is playing at Rockwood Music Hall.  There generally isnt a cover, you can sit down with a drink and listen to awesome bluegrass, soul, jazz or folk stuff. 

Since you mentioned that you're a foodie, have you considered taking a recreational cooking class? There are many in the city to choose from and it's a nice way to spend an evening meeting new people in your class and enjoy the food you make together! Most classes will also serve drinks with the meals. A few places to look into are Institute of Culinary Education, Astor Center, Astor Center, Haven's Kitchen.

I would say head to Brooklyn. The Brooklyn Museum is open late on Thursdays. Fridays you can go to a lovely coffee shop Postmark Cafe and see free comedy. The first Tuesdays of every month DUMBO KITCHEN hosts Dumbo comedy. Go to Vinegar Hill House first for dinner, you won't be disappointed. 

Hi Jen,

Gosh, I'd recommend just about anything. But since I'm a music lover I would try to score a ticket to a performance at the The Metropolitan Opera or the New York Philharmonic. You could also catch a Broadway or an off-Broadway show. There's no stigma of any kind attached to going to performances here solo in New York City. There are also lots of great restaurants where you can dine at the bar. Here are a few: Lincoln Ristorante (on the Lincoln Center campus), Gotham Bar & Grill, the Grand Central Oyster Bar(practically an historic landmark!), A Voce and Bouchon Bakery at Time Warner Center and even Per Se in the restaurant's salon area (no reservations required). Also there are loads of restaurants in Chinatown, too, are so casual that it's not awkward to dine alone.

Levain Bakery,LLC for the best chocolate chip cookies 

I love ramen, so Ippudo, Totto Ramen

Cocoron Soba for Soba 

L'Artusi for Italian food 

Shake Shack would be worth the try if you want a simple but good burger 

Molly's Cupcakes on Bleecker is very good too 

Spot Dessert Bar in St. Mark's Pl 

For Brunch, Jack's Wife Freda in SoHo. It's more for people seeing more than anything else. The food is good too.

Nolita (North of Little Italy) has been my favorite hangout area when I was single in my 30's, and I still just walk around when I look for some fresh vibe and inspiration. It offers plenty of small boutique shops and cool restaurants and galleries spreaded around Elizabeth St, Mott St, and Mulberry St. This area is reminiscent of SoHo in 80's and 90's when it still embraced emerging and hungry artists(now you only can see chains of big name brands in SoHo) but cleaner and quieter version. I think it's a perfect hangout place for a solo female traveler.

I would check out The Slipper Room (The Slipper Room). It is truly a one of a kind theatre-bar experience!

A few of my favorite places...

To Eat and Drink:

Narcissa

Wallflower

Piora

The Campbell Apartment

To Cook/Shake:

Miette Culinary Studio

Sur La Table 

The Wren 

To Explore: 

The Metropolitan Museum of Art

Museum of Modern Art

Solomon R. Guggenheim Museum

To Laugh:

Comedy Cellar

I can't see that Musicals have been mentioned... I'd highly recommend seeing anything on Broadway. You might consider trying to get your tickets for a discount via TKTS Times Square on the day of. Google TKTS, you can't go wrong!

Many of the best restaurants in the city allow you to eat at the bar - it's often the best place to dine, solo or not!  Try Babbo, Minetta Tavern (Their black label burger is something I still dream about - but it's tough to get in, even at the bar), Momofuku Noodle Bar, Má Pêche, Balthazar Restaurant, and many others.  I hear Le Bernardin let's you eat at their bar but haven't confirmed that.  

For live music/theater shows: Joe's Pub http://www.publictheater.org/en/Joes-Pub-at-the-Public/ 

Comedy: Comedy Cellar http://www.comedycellar.com/

Depending on when you are in NYC, some of the museums have live music/art/food events at night: check out Brooklyn Museum's First Saturdays and Museum of Modern Art.

Organize the live events and places you want to check out with theLATER: https://itunes.apple.com/us/app/id929384640

Go to the TriBeCa/SoHo areas and enjoy!