After you receive your reward from the king of Stornway, you should go through the checkpoint in northeast Stornway and go to Coffinwell.
Go out of the town of Stornway and head northeast to reach a checkpoint. There is a gatehouse where one of the soldiers will give you a mission.
After going over the bridge, go north to get to Coffinwell. Be sure to check the bookshelves in the houses of Coffinwell, because many of them have alchemy recipes.
Go to the house in the back of town and speak to the Mayor. Then go to the house just west of the Mayor's house and speak to Catarrhina.
Now go down the stairs, and then go up to the door that is built into the wall with some stairs above it. Talk to Catarrhina and go into the door.
Check all of the bookshelves to learn some recipes as well as the party trick Provoke. Talk to Dr. Phleming, and then go talk to the mayor to receive the Quarantomb Key. Go back to Dr. Phleming and show him the key.
Now you can go to the Quarantomb. To get there, go west from Coffinwell to reach the Western Coffinwell region. The Quarantomb is in the northern part of Western Coffinwell.