Homework Salesman has many locations within it's universe. Listed below are places that are available in the current version of the game.
Merrill - Hometown of protagonist Reniat Leminghouse, her family, and most of the rest of the cast.
Blackbird Forest - The forest right outside of Merill.
Colorous Cave - The cave at the edge of Blackbird Forest. Reniat will have to explore this. It contains six levels. From the entrance, turn left and explore until you meet a guard who will allow you to enter level 2 if you have an Adventurer's Permit.
Runalea Plains - To reach Runalea Plains, enter Colorous cave and go right. The Plains feature beautiful waterfalls, exotic flora, medium to difficult monsters and plenty of buried treasures.