in the last mission you head into a small private jet and can fight in it for about 6 seconds before it gets blown up and you go skydiving out but no the only aircrafts that are flyable are helicopters
Airplanes were fun in San Andreas. They would not be fun in Liberty City. It is way too small with no countryside/deserts to fly over. Where would you land except the airport? The streets are fairly narrow and densely populated with cars and people. Don't worry, I've heard you can steal an airplane from a Sasquatch wearing fingerless gloves in Red Dead Redemption. --- Lakitu is a jerk. He lives in a cloud and throws AIDS at decent, hardworking Americans.
Liberty City only has that one airport and as said before its too small for planes. I wouldn't mind planes on floats though like the dodo I think it was called in the previous GTA games. There's enough water around so that would make more sense.