Usually, your home point (or respawn point) is going to be the city you started off in. After the airships are open to you, you should be able to travel back to Limsa for a fee of 120 gil, if you've gone back to the airship landing (which should also be available to you as well) and talked to the ticketing agent. As I've not died during the airship quests, I can't give you much help. If the game isn't allowing you to go back for 120 gil, then you might want to submit this as a bug. Maybe someone else out there may have had something similar happen to them.