Go to Gant's Gym with the jetpack.

Once inside go into the corner of the gym on the right as just as you enter.

There you should be able to just fly straight through the roof.

Once you are in the glitchy looking place, here comes the tricky part.

You need to go up and up as soon and as far as you can and look around a little bit.

Eventually you should be able to just start exploring more freely and you will see Liberty City.

Liberty City is completely empty - no NPCs, no cars, no nada! Just buildings. It's fun for about 5 minutes.