Manhattan is, in general, very well serviced as long as you live below 110th Street. North of that, things get a bit dicey as it can take nearly an hour to go from 207th Street to Times Square/42nd street on the 1 train due to lack of express trains along that line. (They shouldn't have dropped the 9 train, IMO!) Also, the further north you go, the more affordable housing is but also the less "nice" the area is.
Skyscrapers are abundant below 59th Street (the southern border of Central Park) and then the buildings get gradually shorter as you go north. By the time you get to 110th Street, a vast majority of buildings are short ones, typically brownstones.
If you live in Manhattan, chances are you'll have excellent access to the rest of the city. If you live in the other boroughs, it's a hit or miss. Plenty of huge gaps in the subway system there, but the MTA plugs it up with an excellent bus service. Staten Island? Forget about it. You need a car if you don't live along the Staten Island Railroad corridor. Oh, and the toll on the Verrazano Narrows Bridge is now $14 going toward the island, or $8 on the Goethals or Bayonne bridges.
You give some, you take some. I hope you do get the chance to visit the city sometime, it is a truly amazing experience.