I live about 25 miles away from Manhattan, when people visit and want to go and see "the city" on a budget here's where I take them; (You don't need to do all of this, but it's all good stuff)
Start at Rockefeller Center, see the tree at Xmas time and then hit all the department stores/xmas windows on 5th ave and Radio City on 6th. Don't forget the top of the rock (The GE Building) if the line's not too long, the views are better than the Empire State Building, Bring a Camera, it's worth the $30.
You can walk north to 59th street (central park south / Apple store / Barney's / Plaza Hotel / Columbus Circle and Time Warner Center)
Walk East to Park Ave and and then South towards the MetLife Building, Continue down park ave until you Walk underneath the Helmsley building breezeway (New York Central Building). Then Walk into the 45th street entrance of the Metlife Building and straight through the lobby, this will take you directly into Grand Central, go down the escalators and take it all in, junior's cheesecake is there as well as other great stuff like the whispering gallery outside the oyster bar, Vanderbilt Hall and Another Apple store.
DOWNTOWN (Skip this if you want, but it's worth doing)
When you're done in GCT and if you're feeling ambitious, you can find the subway and jump on the 5 express train to Bowling Green station, which is a short walk to battery park which has great views of the Statue of Liberty, if you've got an hour to kill, hop on the Staten Island Ferry (it's free) for great views of the city from the water. When you get to Staten Island get back on a ferry to the city and enjoy the views again.
When you're done at the battery walk north on Broadway to Wall St. and Trinity Church, If you keep walking east you can find the South Street Seaport, Just north of the South Street Seaport is the Brooklyn Bridge (a great walk with great views, especially at dusk) At the foot of the Manhattan side of the bridge is the City Hall, walk to West side of City Hall to the "R" Subway Station.
Hop on the R Train To Herald Square. At the surface you'll find Macys at Herald Square (Thanksgiving day parade...), When you're done At Macy's walk east to the Empire State Building (the lobby is nice). When you're done at the Empire State Building walk north 6 blocks to the New York Public Library and Bryant Park. Then walk a Block west to 40th and Broadway to the "Times Square" R train station (see TS if you must...) and get on the R train back up to the Lexington Ave stop and walk 3 blocks back to your hotel.
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