If you talk to all the people in Temple Town, you'll hear a bit about Claw and Temi - two more people who will ultimately join your party.
You'll also hear a lot about job classes! Yes, you can change jobs in Temple Town; just not yet...
Enter the temple and go all the way to the back room. There you'll meet Temi, who will say that if you can find the Tower Key, she'll join your party. The Tower Key just happens to be in the tower with all the monsters, so you'll need to go there before Temi will join you.
You can also talk to the Priest here, but he'll just tell you that you can't change jobs right now because there are monsters in the tower...
There's an Alchemist in the southeast corner of town who says if you find something strange, to bring it to her. In the Dungeon of Trials (just east of Temple Town), you can find Red, Blue, and Yellow Odd Objects, and if you bring these to her she can combine them into different items.
You can combine up to 20 of each color, but only certain combinations will actually yield any results.
When you're done here, head northeast toward the E. Tower, but stop along the way at the Traveler's Inn.