Written by MSG Commander
After you defeat the Demon King, you'll be prompted to save your game, and then you can either continue, and do the post-game content, or reload your data for a new game+. (Note: the story does not change if you choose new game+, but all of your skills, gold, items, etc., carry over.)
If you choose to continue your game, there's a short bit of content in the Crystal World (though it may require several hours of grinding to beat the final boss).
There's also a bonus side quest in the Lost Kingdom of Fura (talk to Matt to unlock it).
And of course, if you haven't already done so, there's the Adventurer's Cave, and the Water Temple (Floors 4-7).