So once you hit level 50, you do not want to do your story because the story barely gives you any experience and will require you to waste your dungeon runs (it will not reset the dungeon rewards like it did when you hit level 50). Instead, the fastest way to level from 50 to 60 is from killing World Bosses.
You can find the schedule here
Take a look at this guide made by Suzukinobuko here
To summarize, craft foods that give EXP (in cooking) if your rank is high enough, and use them while killing the bosses. Killing the bosses while in a party also gives you bonus experience, so ask around if you're not in one.
The most popular bosses are Giant Turtle and Amadon specifically, so make sure you capitalize on them!
The general procedure is...
- Look at the schedule and find a boss that is up or is about to be up and go to channel 1 or 2 where the boss is.
- Consume the food that gives XP
- Form or join a party
- Kill the boss and then check your map. Howevering over the boss icon will show you the channels where the boss is still up.
- Go to the next channel where the boss is still up. If there are not enough people, you may want to go find another boss that is up or is about to be up. You can use the /nextchan or /nextchannel command to go to the next channel, or use the /movechannel 5 for example to go to a specific channel.