As promised (and by popular demand), I finally finished my Highly Subjective List of Favorite Places in NYC.  I tend to like the places that are old and/or unusual, rather than those that are particularly trendy and expensive.  Fair to say, I haven't lived there for three years now, so your mileage may vary.
 
Museums:
 
Metropolitan Museum of Art, Friday or Saturday evening (until 9PM, get there by 7 at the latest). "Ground" and "first" floor are given in non-American style here; the equivalent American terms are "first" and "second" floors. Not to be missed:
  • Classical music in gallery above foyer with drinks (splash out on some champagne!) (first floor)
  • Annenberg Nineteenth-Century European Painting and Sculpture Galleries (first floor, to left). Don't miss the Rodin, extremely well displayed.
  • Rooftop sculpture garden (another bar here!) from lift on ground floor. (There is another excellent sculpture gallery and a cafe near this ground floor lift)
  • The American Wing on ground floor (a fantastic and peaceful room with a few fountains and Tiffany glass, among other great bits)
  • Egyptian Art: finish off at the slightly spooky Temple of Dendur and among the mummies.
Guggenheim: corkscrew-shaped museum with exhibits displayed on one long ramp. Either take a lift to the top and work down or even better walk up the ramp examining works in detail and then coast down quickly from the top just taking in your "greatest hits". If you take in the galleries off the main ramp there's generally too much to take in on one visit, the main attraction is really the central ramp.
 
The Frick Collection and the Museum of Modern Art both have great permanent collections in interesting spaces.
 
East Village: my old area, loads of great restaurants and bars
Restaurants
Curry Row/Little India: (6th Street bet. 1st and 2nd Avenues): food is Bangladeshi which is somewhat different from what is found in the UK, if you go pick one with live bongo/sitar music in the front window, which is very enjoyable. We recently went to "Calcutta" which is fairly representative. Be amazed by the amount of kitchy decoration and fairy lights in most of them, particularly the two around the corner on 1st avenue. There's also an area called "Curry Hill" near Murray Hill with another gang of Bangladeshi restaurants. The most interesting of these is by far Vatan (3rd Ave. and 29th) which has cozy seating in little "huts" and serves you loads of unusual Indian hors d'oerves for a fixed price until you can't eat any more.  http://www.villagevoice.com/bestof/2000/detail.php3?id=2406
 
Dok Suni: Korean "home cooking" on 1st Ave. between 7th & 8th streets, have some hot sake and try the bulgogi (like fajitas but with lettuce leaves in place of the tortilla, make sure to ask how to make them) or the wonbok kimchee. A favourite of Quentin Tarantino's and still quite trendy, for what it's worth. Otherwise check out little Korea on 32rd street bet. 5th and 6th, though I think Dok Suni is generally better. http://www.menupages.com/restaurantdetails.asp?neighborhoodid=0&restaurantid=5129
 
Veselka: 2nd Avenue and 7th Street, great Ukranian food, New York's best borscht (beet soup), also great veggie stuffed cabbage, potato pancakes, pierogis, etc. Seventh street in the East Village is largely Ukrainian/Polish, Kiev across the road is another famous Ukranian spot. http://cuisinenet.com/info/cnetrst-617/?v=237
 
La Paella: 9th Street between 2nd and 3rd Ave: great tapas, very romantic with roses on the ceiling. Despite the name, ignore the paella which isn't amazing. The broiled calamari (calamari a la plancha) is wonderful, as are the gambas al ajillo (shrimp in garlic), the pulpo (octopus), serrano ham with melon, and the stuffed mushrooms (championes). Ceviches and sangria here are great too. There are also loads of other great places to eat on this (very NYU student) part of 9th Street, including some of NYs best sushi restaurants.
 
Benny's Burrito's (6th Street and Avenue A): Great mexican food, with large windows overlooking the ebb and flow of life on Avenue A.
 
Nino's Pizza: Corner of St. Marks (8th Street) and Avenue A: my personal favorite late night pizza slice joint, just cheesy and greasy enough to soak up all the beer.
 
Bars
Lucky Cheng's (1st Avenue and 1st Street): Actually a Chinese Restaurant/Tiki Bar/Karaoke (on some nights) with, well, waitresses who are really waiters. Generally a fun place on a Friday or Saturday night, loads of hen parties and the like. A good area to go out in general, with DBA and other good spots across 1st Avenue, and the entire Lower East Side just south across Houston Streethttp://www.luckychengs.net/home.html
 
Burp Castle (7th Street, bet 2nd and 3rd Aves): Temple of beer worship. Seriously. Oriental carpeting, fantastic medieval-style murals, and a monk who shushes you if you are too loud to properly appreciate your beer.
 
McSorley's Ale House (also on 7th Street bet 2nd and 3rd Aves): oldest bar/brewery in NY. Tiny glasses of beer, usually only ordered in pairs. All of two choices are available: light or dark. Previously (not all that long ago) forbidden to women.
 
Don't miss Alphabet City for a spectacular variety of bars, restaurants and nightlife, too numerous to mention--particularly Avenues A and B between 10th and Houston.  Also try to get down to the Lower East Side, below Houston, for some great grunge nightlife, particularly Orchard Street and points east between Houston and Rivington.
 
Greenwich (West) Village
Restaurants
John's Pizza/Joe's Pizza: don't miss out on NY style pizza: John's (Bleeker Street) is considered the best in Manhattan (coal fired brick oven, no slices), while Joe's (corner of Carmine and Bleeker Streets) is just perfect for a late-night slice or two. Avoid anyplace called Ray's, Original Ray's, Famous Original Ray's, etc. as they are all neither famous, original, nor pertaining to anyone named Ray (nor particularly good).  The "official" best pizza in NY is Patsy's in Brooklyn, right over the bridge.  And my personal favorite for late night cheesy/greasy slices is Nino's on the corner of St. Mark's and Avenue A.
 
Grey's Papaya (6th Avenue and 8th Street, also other locations): another NY institution, the best NY hotdogs and slightly bizarre soft drinks, super cheap. The hot dogs taste great with saurkraut and mustard after a night of drinking, can't say much for how they taste at any other time. New York's answer to a late night kebab.  http://www.epinions.com/rest-Restaurants-All-Gray_s_Papaya/display_~reviews
 
Bars
Tortilla Flats (Meat Packing District, Washington Ave. & W. 12th St): Possibly the most fun bar you can be in on a warm Friday night in NY, although pretty good any other night as well. A Mexican restaurant that is famous for kitshy decor, an Ernest Borgnine memorial wall, Bingo on Mondays, hula hoop contest on Tuedays, and the best damn jugs of margaritas anywhere north of the border. My personal recommendation is to get a few jugs of margaritas (on the rocks, as frozen are too hard to drink at length), stand or sit at the crowded bar (ignore the temptation of getting a table), and enjoy the variety of pop and metal music, the bizarre bartenders and the swirl of life around you. Make sure to check out the refilling of the margarita fountain and don't be surprised if you make a few friends here. http://www.tortillaflatsnyc.com/history.html
 
Hogs and Heifers/Red Rock West: Work your way north up the Meat Packing District past Hogs & Heifers (Washington Ave & 13th St), an extremely touristy "biker bar", to Red Rock West (10th Ave & 17th St), southern rock/biker establishment with loads of character and barmaids dancing on the bar. Red Rock West is in my humble opinion the bar that "Coyote Ugly" was based on, but there was already a movie with the name "Red Rock West" so they chose the (admittedly funnier) name of an entirely different bar on 1st Avenue that subsequently added dancing on the bar. Red Rock West tends to have the best bartop entertainment with fire breathing, shots poured directly (without a glass), water spraying, and some other quasi-legal behavior. http://www.nycbp.com/bartenders/bar9/index.html
 
Duplex: (7th Ave. and Christopher St): old school cabaret/piano bar. Show tunes, sing-a-long and the like. Very good for a laugh, very typically Greenwich Village, a bit touristy.  http://www.theduplex.com/index.shtml  Brandy's (upper east side) and the Oak Room at the Algonquin are more traditional/romantic piano bars/cabarets.
 
Chumley's (86 Bedford St, though there is a better entrance hidden around the corner on Grove Street): old speakeasy in an obscure residential area, enjoyably difficult to find especially if you come in through the garden entrance (there are two ways to enter, the second one is highly unexpected), good food and ale and very comfortable (a trademark is that there are usually a few large dogs lying about).  Apparently the origin of the American expression "to 86", as in "86 that order".  http://www.wguides.com/city/33/126_209804.cfm, http://www.pubcrawler.com/Template/ReviewWC.cfm/flat/BrewerID=1149
 
Culture Club: Very touristy and cheesy, 80's discotheque.  Unfortunately its sister club, Polly Esthers, which did 70's music, recently shut down.
 
There are just bazillions of other great spots too numerous to mention (Asia de Cuba, Morgan's Bar, etc.) but I have to stop writing sometime before I end up writing the next NYC guidebook.