As touristy as it sounds, one of the first things NYC tourists should do is take a bus tour to orient themselves.
As small as Manhattan is, it's packed with neighborhoods that each have a different feel. Some may be more to your liking than others, and this is a great way to find out where you might want to spend more time. And it's really the only way to see a lot of destinations in one day. Trying to do each by subway can get exhausting.
Hop on hop off is better for most people than a guided tour--you may want to skip a destination, or you may find one you like and decide to stay their all day. This way you have a choice. Buses arrive fairly frequently at each destination.
There are various companies to choose from--the best is the Gray Line Big Apple.
Also recommended are the Circle Line boat tours, which are not as elegant or exotic as the Classic Harbor Line Schooner tours, but nonetheless can be lots of fun (or so I hear--I haven't been on the Circle Line yet). The Circle Line departs from Pier 83 at 42nd Street & 12th ave on the Hudson River., and which run from 75 min-3 hours ($24-34), April- Sept their ours are: 75 min tour: Daily: 11:00am; 1:00pm; 3:00pm . 2 hour tour: 11:30am; 3:30pm . 3hour tour: 10:00am; 12:30pm; 2:00pm; 4:30pm .
