Another possibility is to join a Free Company who has a house in either the Goblet (Ul'dah) or the Lavender Beds (Gridania).

If that Free Company has placed a miniature aetheryte in their estate, you'll be able to teleport directly there from Limsa Lominsa even right at the start of the game as soon as you join (the option appears automatically in your teleport list), and hence just have to then head out to Ul'dah/Gridania and attune to the aethertyes there to access them whenever you feel like even before you've gained airship travel.

This also works in reverse for players who start in Ul'dah/Gridania and join a FC based in Mist (Limsa Lominsa) before they get their airship pass.