A successful landing at LGA or TEB, as many have already noted, requires crossing a precise point in space at a precise speed. A hundred yards or so short would likely lose all aboard.
Exactly. I'd speculate that Capt. Sullenberger's glider experience did influence his decision not to try for La Guardia or Teterboro.
Fact is, to achieve a precise landing in a glider, the glidepath can be very effectivelly controlled with airbrakes that can be instantly set to any desired position during the final.
In an A320, even if the crew could rely on having power for the flight controls (which they couldn't) the time required for any flap setting change makes glidepath control imprecise. The only remaining trick, a sideslip, would require some previous training experience to get an idea of its effectiveness.
So even if they had been able to set up an approach, the risk of either an undershoot or overshoot (with no guarantee of available brake pressure) would have been significant.