I know my response is long, but filled with some good stuff...
I have been going to NYC 2 to 3 times a year since 1987 (OMG is that 25 years already??!!??) and always go by myself (no asking my partner are you enjoying the show? what do YOU want to do today?).
My primary advice do tourist stuff if you want/need to, but also do stuff you would do if you lived there (easy for me since I am now there every Nov, Jan and Jun for 6-8 days each time).
Here are some of my favorite things to do:
(1) For hotel, I stay at the Best Western President Hotel in Times Square but closer to Hells Kitchen one block from a Food Emporium grocery store and 12 blocks from Whole Foods. I get my dinner at Whole Foods most evenings and take it back to my room. Believe it or not, one block either way makes a difference. I get a fridge for my insulin (diabetic here) and use it to stock breakfast stuff (cereal with milk, fruit, yogurt) and cut down on the food costs.
(2) If you really LOVE theater (and if you are on this site you probably do), get theater tickets for most every possible time Tu-Sun evening at Wed/Sat/Sun matinees (some Bway shows and a most off-Broadway shows have Sun eve performances).
(3) If you cannot afford to get tickets in advance, use the TKTS line. If paying full price for a show, try getting those for higher demand days/nights like weekend evening and matinees and then TKTS for off times like weekday evenings and matinee. If using TKTS, I have started going to the booth a little before curtain time, the lines are shorter and you might actually score a better seat at the last minute rather than hours in advance (I dont do TKTS that often anymore).
(4) Utilize the discounts on this site, Playbill site or BroadwayBox.com (my personal favorite). You can get up to 45% off a ticket with advance purchase and still select the seat you want (depending on the theater).
(5) Try some off-Broadway theater, and if you can, go early and experience the neighborhoods around the theater (Union Square has a lot of little theaters and the area is close to NYU and a lot of fun to hang out in).
(6) Before you get to NYC, check the percent attendance and average ticket price on this site or Playbill site (hint: Just because it is higher occupancy does not mean they bypass TKTS). Plan accordingly, more popular shows may be available at TKTS early in the week or weekday matinee. As noted above, if using TKTS, I tend to go later before showtime when there are no lines and have scored some pretty awesome seats for decent shows (but be realistic about what you may get it could be aisle seats in orchestra or off to the side with obstructed views that is part of the fun).
(7) Pick 2 or 3 things you want to do on the visit (Empire State Building, Rockefeller Center, etc). Try something not totally touristy if you want the more offbeat. I like to go to the Metropolitan Museum they have a GREAT cafeteria in the basement and I go for lunch and then browse some of the art (I go every visit so I pretty much concentrate on a temporary exhibit when I go) and I also shop in their store (scarves for the women in my life, bargains for me). I also like to peruse the MOMA Design Store (across the street from MOMA) and the MOMO bookstore.
(

Get the Chronicle Books Walking Tours of NYC there are about 32 cards with different interesting walking tours of various areas in the city each card has a map of the tour route and highlights not to be missed. My favorite walk is from the Metropolitan Museum down along the park (and weaving in and out of it) down and over to Columbus Circle to Whole Foods.
(9) Go to a flea market or a street fair they are easy to find online and check out the bigger more established flea markets. I know you are on vacation and cannot haul stuff home, but it is interesting and fun and not expensive. Street fairs are fun and give you a sense of the corresponding neighborhood you can also find some really cool stuff for Christmas presents (I do a lot of my shopping in NYC at things like street fairs for the harder to buy individuals.
(10) Treat yourself to something fun, I get a massage from a massage therapist who works out of his apartment in the West Village. The space he works in is dedicated to his massage clients so it is a very comfortable and relaxing environment.
(11) Use the subway if you have time, a taxi if you are a little rushed for time. Taxis are not terribly expensive but can add up. Know that it is hard to get a taxi at around 430PM in some areas as they are changing shift (found this out the hard way one day while in a hurry to get back to the hotel in the rain).
(12) I have never done the tour bus thing, but other posters are correct. You can pay one price and stop and go as much as you want from one site to another.
One of the best pieces of advice I can give you, start early but end early if you are seeing theater that evening. There is nothing worse than an overactive day that causes you to run out of steam half way through a show. As noted previously, I have diabetes and that combined with touring fatigue has caused me to drop off during a show and miss the most exciting part of my vacation THEATER!!
Let me know if this helps or if you need more info.
ENJOY the trip - NYC is one of the greatest cities to vacation (and I live in SF). I only go there - I have family in Buffalo and Syracuse so I wrap a family visit with my NYC fix. I wish I could live there and since I don't going 3 times a year allows me to "pretend" that I do and I LOVE IT!
Lastly, you need to be wary of your surroundings, but New Yorkers are really great, fun, helpful people who appreciate someone who is polite and respects their city. I never feel uncomfortable or unsafe when I am out and about. There was a time that Times Square touching on 8th Avenue was sketchy, but those days are over. Hells's Kitchen (neighborhood to the west of Times Square) is just a name of a neighborhood and it is a really cool funky area just over from Times Square and I LOVE IT. Try yhe Galaxy Diner on 9th Avenue at 45th (I think) for breakfast. Cheap and fun atmosphere.
Updated On: 2/8/12 at 05:11 PM