Take the boat to the Statue of Liberty and Ellis Island. Get there early, and I mean early, aim for the first or second boat out; the line increases exponentially as each half hour passes.
Go see a Broadway show using 'rush' tickets. These are 'day of show' tickets that are bought in person at the theater in question in the morning on the day of show. Pick a show you want to see, and call the box office and ask if they have rush tickets available, and how to proceed about getting them. They usually cost about $25, a substantial savings. Wednesday matinees are good bets for excess seats. We got front row for Chicago. That was too close. A lot of the magic disappears when you can see the spit come out of the actors mouth and the dirt on the soles of their shoes as they dance. Shows that have been running for more than a year usually have rush tickets available.
Wander Central Park: don't miss the Zoo and the bandshell by Bethesda Fountain, and also see Belvedere Castle. The Wisteria arbor is beautiful, too.
Go to the Metropolitan Museum of Art, located in Central Park on Fifth Ave. Explore the Medieval wing and be amazed by the Studiolo. Also check out the American wing with it's beautiful Tiffany windows. Despite what they would like to have you believe, admission is by donation. That means you can give them a dollar or 5 dollars, not the huge amount they suggest on the sign by the admissions. Closed Mondays.
Go to the Natural History Museum at 80th and Central Park West. My favorite display is the hall of gems and minerals, and the Hayden Planetarium. They have awesome dinosaur casts and a really scary cast of a giant blue whale hanging from the ceiling. Lots of Native American artifacts and moth-eaten animal displays. Kind of creepy and kind of fun. Check out the extinct fish fossils for a good laugh. Feel relieved that the Earth no longer harbors elephant sized sloths. Buy yourself a cool souvenir from the Rose Center for Earth and Space. Open daily.
Go to the Cloisters, the Medieval annex to the MET, located in Fort Tryon Park, a beautiful terraced park on the Hudson in upper Manhattan. You'll never believe you're in Manhattan. Very peaceful. View of woods in NJ across the river donated by Rockefeller when he endowed the Cloisters. Closed Mondays.
Explore lower Manhattan on foot from 8th Street on down. Wander around at random and know you cannot get lost because you are on an island. Pass through Greenwich Village and the lower Eastside on your way to:
The Southstreet Seaport. Gawk at the views.
Go to St. Mark's Place and sort of relive the 70's.
For classic NYC souvenir shopping skip the tourist trap shops of Times Square, and go to the source: Mulberry Street in Chinatown in lower Manhattan. Lower prices and bigger selection.
Do NOT buy designer sunglasses from street vendors and do NOT play Three Card Monte no matter how many times you see another guy show you how easy it is to beat the Monte dealer.
OK, that's enough from me, please add your favorite Manhattan activities so that those visiting the hot dog can make the most of their time there.