Tripadvisor's number one rated thing to see at the time of this writing is The Manhattan Skyline. The East River Ferry provides an excellent and inexpensive means to experience this. The ferry costs $4.00 and during peak schedule times leaves from each stop about 20 minutes apart.  Riders will find the trip relaxed and pleasant. They can sit inside (in case of inclement weather) or outside (when the weather is nice). 

The Ferry connects East Midtown at 34th Street in Manhattan with Long Island City in Queens, various points in Brooklyn, including Williamsburg and DUMBO, Governors Island and South Manhattan at Wall Street / Pier 11.

The Ferry features double-decker catamaran vessels that can transport 149 passengers and also provides bike racks on the boat that can carry a small number of bicycles (there is small surcharge for bike-on-boat riders).

There is more innformation at the Ferry's website:

There also is a PDF map of the Ferry's route: 

One way to experience the ferry would be to walk across the Brooklyn Bridge, lunch and stroll in the DUMBO neighborhood of Brooklyn, and then catch the ferry directly under the bridge for a leisurely and scenic return to Manhattan.