The northern end of the airspace over the East River where Cory Lidel and his flight instructor were flying on Wednesday is said to be a fearsome, narrow corridor. This from the NY Times.

The northern end of the airspace over the East River is a
treacherous, narrow corridor often filled with helicopters ferrying
tourists, business people and traffic reporters along the edge of
Manhattan. Small planes like Mr. Lidle’s are allowed to fly through the
area at low altitude, but several pilots said they did not dare because
it could be crowded.

The spot where Mr. Lidle’s plane, a
single-engine Cirrus SR20, struck the apartment building on the Upper
East Side is near the end of the “uncontrolled” corridor at the edge of
the airspace governed by La Guardia Airport. Inside that corridor,
small planes and helicopters can fly below 1,100 feet without getting
clearance from air-traffic controllers. Using what are known as visual
flight rules, or V.F.R., they assume responsibility for watching out
for other aircraft and structures and avoiding them.

Mr. Lidle’s plane was traveling north before it crashed into the
north side of the building. Officials said they did not know if the
plane had been turning around when it crashed.

To continue
north beyond Roosevelt Island around 86th Street, pilots must radio the
La Guardia control tower and seek permission. Controllers usually allow
pilots to do so, and the Cirrus would probably have received such
permission, said William S. McLoughlin, head of the La Guardia tower
chapter of the National Air Traffic Controllers Association.

But
many pilots choose to make a U-turn instead, several pilots said
yesterday. Still, they said, reversing direction there , which normally
involves a turn to the left, can be challenging. Yesterday afternoon,
according to the National Weather Service, the wind was blowing from the east at 14 miles per hour, conditions that would have made the turn wider.