You can actually walk / run between the cities but due to the high level mobs on the way you're mostlikely get killed in about 10 seconds. In Griday there is the main story quest called "Gridania Envoy" which would give you the airship pass and first free trip to Limsa Lominsa and Uldah as part of the quest. After that you can freely purchase airship tickets to any of the main cities (200 gill) or use favourite aethernets to teleport directly about 90 - 250 gills depending on location. The main story quest's are those with flame frame around the exclamation signs.