You're now in Riverside. First, go to the Inn and sleep. There are a few items hidden in the Inn also.
Beside the Inn is Moryt's house. Snag the Elixir in the pot. Now go to the Palace.
To the left, downstairs, you'll find the Scroll Dealer. Buy a Cure Scroll from him. Go back up the stairs and to the right, downstairs to the prison.
There is a secret here. Find the opening on the South wall and get the weapon in the chest.
No go back up stairs, North, and talk to the mayor. He'll send you on a mission to the Haunted Mansion to put an end to the monster problem.
To the East of the Palace is the Captain's house. Upstairs, you'll find some cash in a pot.
To the North of the Captain's is the Old Man's house. If you got both rings in the forest, he'll give you two scrolls. You can use scrolls to learn spells. I find it best to give one character white magic and one black magic, but you can use them on whoever you want.
Beside the Old Man's is the equipment shop. Buy a Helmet and a Ghoul Sword. The weapon you found in the prison is better than anything here, and there's a better piece of armour you can get for free (see below.)
Head South of town and go left at the fork in the path. You'll find an Elixir on the beach.
Now go back and go right at the fork. Outside of the Haunted Mansion there's a chest with armour in it.
Before going into the Haunted Mansion, I find it best to level up to level 2. You'll need to fight a few battles in the forest to do so unless you're there already (not a lot... don't worry.) After that, save at the Inn and head to the Haunted Mansion.
Don't forget: you have to read your scrolls before you can use their spells.