There is a quest at the beginning of the questline in Azsuna that allows for some extreme Experience gains very quickly, and with this method you can easily level up every 30-60 minutes! The quest needed is called The Scythe of Souls, which is one of the very first quests, so if you already did this, sorry, but this method will not work for you.
Anyway, here's the method:
Start by downloading and activating an add on called Cross Realm Assist. Now log into the game and click on the three crystals required for the quest. This spawns a big mob that is actually really easy to kill, but awards you with 5k XP! After he is dead, press the Quick Join button on the Cross Realm Assist Add on to hop onto a new server. This will reset the quest, and you are able to click on the three crystals and spawn the big enemy again for another 5k exp. He is usually alive on all the realms, but if not, just use the button again to go to another server.
Now you simply need to keep doing this and getting 5k exp every time you kill the boss, and you will level up in no time!
The downsides to this method is that you obviously don't get any rep and quests completing in the Legion zones, but don't worry, in patch 7.1 World Quests will be automatically unlocked for alts once they reach level 110, so no need to quest in every zone anymore.