chocobo porters have a limit as to how far they can go. the exact distance is kind of ambiguous so you gotta check with the porter him/herself to see if it allows you to travel to your desired destination, ad obviously you can use a porter from vespar bay to quarrymill.

for fast travels:
1. look up your destination, take an airship to the city, and porter there if it is near, or teleport from that city, which will cost way lesser than teleporting it from the other end of eorzea.
2. if you are doing the main story line, research beforehand where you are likely go to move to. so far, until up to haukke manor, it benefitted me greatly to set my homepoint at gridania. home points speed up travelling as you could just use Return instead of using airhship