You can begin on 72nd Street and run beyond Columbia University. It's a great run not to crowded and nice greenery.  

 
Enjoy!

The Hudson Greenway right along the Hudson River will take you up to Riverside Park mentioned above-  you can run North towards the George Washington Bridge or you can run South towards downtown-  it's a nice option and mostly flat, however, I think the best place to run in New York is Central Park-  a full loop of the park is about 6 miles-  though it's fairly hilly especially the top of the park around 110th were you will have to deal with the Harlem Hills-  if you want to avoid the toughest hills you can cut across the park at the 102nd street transverse which will make it about a 5 mile run, or you can just do the lower loop (cutting across at the 72nd Street transverse-  about 1.7 miles)-  or a lot of people enjoy the 1.5 mile loop around the Reservoir in the Central Park which is also very scenic

On the East Side of midtown, you can access the greenway heading north that runs along the East River by running to 60th Street. There's a ramp that runs next to the 59th Street Bridge that turns north and you can run up to about 125th street (roughly 3.5 miles). Depending on the time you run, it can be fairly quiet but not creepy/deserted. It's lovely with the breeze off the river and the views are nice.

Likewise, you can access the greenway heading south if you enter at 34th Street. this can take you down to the tip of the island (Battery Park) with views of the Statue of Liberty. You will pass under the Williamsburg, Manhattan, and Brooklyn Bridges along the way. Just under 4.5 miles.