Having grown up in Brooklyn now living near Boston, and with family still in Manattan some tips:
- Statue of Libery and/or Ellis Island are good day trips, but will be most of the day. Get tickets in advance on line as the lines to buy them on site can be hours long and the boats sell out.
- Ground Zero, haven't been down that way since July and it is probably still surrounded by a large fence, basically nothing to see from the street. You can buy tickets, also in advance, for access to the reflecting ponds inside the construction site. Don't waste your time trying to get them the day of. Tickets are limited so the crowds don't become enormous.
Coney Island can be fun, that said it also isn't Disney World. The amusement park rides are decent but geared for sub-8 year olds, with the exception of the Cyclone, which is a classic wooden roller coaster and a national landmark. A brief walk along the water is the NY Aquarium, which is a great way to spend a day. Multiple subway lines go right to the Coney Island station, but it's a 90 minute ride from Mahattan so its a commitment. Not my first choice if you have one day in NYC and its your first time there. I think the boardwalk is still damaged form the hurricane.
With one day, I'd encourage:
- Central Park, walk inside the park along the Fifth Avenue side. Central Park Zoo (very nice) multiple playgrounds, and further North Belvedere Castle. Move West there and you can get to Strawberry Fields (John Lennon) and multiple play areas. There is also a large carousel restored a decade ago near the SW corner of the Park that is a good diversion. Google Central Park walking tours....they have free guided tours of areas of the park 365 days of the year. I've taken a few and they are interesting. You can also rent model sail boats and sail them in the pond:
http://www.centralpark.com/guide/sports/model-sailboats.html. This is kind of fun, actually.
Museum of Natural History is on the central Western edge of the Park (77th street I think) - .Good dinosaur exhibits, minerals, and the Hayden Planetarium. The Metropolitan Museum of Art is a little North of the sail boat pond. Youo could spend a week there.
Going South from there is the Intrepid as suggested before. Can be pricey if you are not into fighter jets and WWII aircraft carriers.
South East from there is Times Square, now closed to traffic. There are loads of chairs and bistro tables, plenth of peole watching. Disney *has* moved in here so it is all the same chain restaraunts you get everywhere else plus a few things like a giant (the largest maybe) Toys r US and a huge M&M store.
Going to the bottom of the island is South Street Seaport although this still may be closed form the Hurrican damage. Food, and old wooden sailing ships. On the east side of that is Battery Park City. That is where the West Side walkway starts, with that you can walk from the Southern tip of Manhattan to I thknk 86th street. Plenty of things to see just walking - all very safe.
A lot of people visiting will buy tickets on the GrayLine hop-on hop-off double decker tour buses. The have fixed routes to major tourist spots. They are good because you can use them in lieu of taxis and mass transit. One ticket you ride all day.
Walk Fifth Avenue South from 59th and 5th to St. Pauls Catherdral,, about 15 blocks. St. Pauls is a gorgeous European style cathedral, Fifth Avenue has all the high end stores like Tiffany's worth gawking at, and across from St. Pauls is Rockefeller Center where the ice skating rink is, although that is closed by now for the summer.
Empire State building is always an attraction...its open until 2:00 AM and at night its is pretty cool and quite romantic.
Re "cheap Lodging" in NYC you get what you pay for. There aren't any hidden gems for $79/night. Try Priceline and see what you get. I have done OK here with rates and its a decent enough hotel in a good location:
http://www.roomstays.com/hotel/643043
re theaters look for this kiosk in Times Square
http://www.entertainment-link.com/tkts.asp?utm_source=msn&utm_medium=cpc&utm_term=tkts%20tkts&utm_content=847107252&utm_campaign=12210703262. Need to buy same day, are 50% off.
Go for at least one decent meal - McDonalds in NYC, really?? Look for pre-theater "Prixe Fixe" (pronounced "pre fix") dinners. These are usually between 4:00 and 7:00 PM, offer several three or four course options, and are at a fixed price. Look at Cafe Un Deus Trois near Times Square. Its a classic and reasonably priced, you can show up in jeans, family friendly, and they give every table crayons to draw on the table cloths!
http://www.cafeundeuxtrois.com/index.html . I'd take a shish kebob from a food cart over McD's any day of the week. Another option is Bleeker Street in the Villagejust east of 6th Avenue (subway to West 4th Street station). Get a sidewalk table and if the weather is nice you can see a few the characters promenading.
Lastly, don't walk around petrified of getting robbed. Crime is the lowest its been in 40 years and it is stunningly safe and clean. I've taken people there on business who have been around the world butu never to NYC before and they leave awed by how clean, polite, and well run the city is. A far cry from the late 70's and early 80's when it saw its darkets days.
Maybe some of this works for you. Let me know if you need more details. Google NYC walking tours, Grand Central Station walking tours. If you have 24 hours in NYC going to Montauk is a waste of time.
Be prepared for crowds. Come noon on Sunday on a nice day *everything* will be crowded. It's an aspect of the city.
Mike