After you receive your reward from the king of Stornway, you should go through the checkpoint in northeast Stornway and go to Coffinwell.
If you haven't already, exit 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 you go over the bridge, go north to reach Coffinwell. Be sure to check the bookshelves in the houses of Coffinwell, because many of them have alchemy recipes.
Go to the northernmost house in the town, go upstairs and go to the right, and speak to the Mayor. Be sure to read the bookshelves behind the mayor to learn new recipes, and check the cabinet in the room north of the mayor to get a Mini Medal. Then go to the house just west of the Mayor's house and speak to Catarrhina. Before you leave, check the bookshelf in Catarrhina's house to learn some new recipes.
Now go south and down the stairs on the right, then go north and talk to Catarrhina, then go through 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 and say Yes 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.