For A whole lot of quanta the king will let you teleport wherever you want.
There are stables filled with ridable eagles, they are extremely expensive to ride though cheaper then the Aether and will get you anywhere, safely in a single turn.
No king, action ability. Dark Teleportation. Demons will offer you their services, taking you wherever you want to go instantly for a steep price. But be weary, there is a chance you may arrive with one less card in your vault.
The Lord of Death will allow you to travel through the realm of the underworld for free, but be warned, fierce beasts lie here. (Fight one Level 5 AI with your deck. If you win, you get through without lost, you lose, three cards are lost when you pass through. Prove it with a timestamps before and after Screen Shots. Battle must be on the hour or at least close to it in order to make it hard to cheat.)
Gnome low ways (Gnome tunnels to other cities but only cities allied with earth. Half Travel, low fee.)
The mad wizard of entropy will teleport you to a random location on the map for free.
Hot Air balloons cut travel down by two turns. Moderately expensive.
For a moderate cost you can have a momentum spell cast on you by the king's powerful wizard. Allows you to accelerate at a constant rate to infinite speeds. Makes it so you can get anywhere in exactly three turns.
Horse, reduces trip by two turns. Low cost.
No king, they actually have an action ability to sacrifice one card to the gods to go anywhere they want instantly.
For a moderate cost, you are hastened you can get where you need to go three turns less then you would have otherwise. However, you will be unable to collect resources during this period and for a turn afterwards as you try to readjust to normal time.
A ship can take you down rivers to various destinations for a small fee, though the options are limited. Twice as fast as normal travel though.