Tyria finds very weird that the emperor would choose her for some kind of very important mission. Nah, this is not happening, she thinks. Since she doesn't know much though, and since nobody seems to know more than she does, she decided to lay low and see what happens.
She gave back his ring to Fargoth, investigated the tax collector's death, found his body, gave the money back and the tax record to the authorities but she didn't punish the murderer; not her job she decided.
Then she went exploring the neighborhood, gathered a lot of alchemy ingredients, killed monstrous slaughterfish, muccrabs, rats; someone fell from nowhere almost on her shoulders. Thanks to all this agitation, her skills improved quite nicely and fast!
More importantly, she freed three slaves she found in a nearby cave. She left the slavers alone though, keeping them for later.
She chose a job for herself and took on alchemy.
Now, she's going to keep exploring around until she feels ready to accomplish the task she was apparently chosen for and go to Balmora.
Note: when levelling up, I chose to give points to skills she actually used; I won't give points to a skill that governs persuasion, for example, if she never used persuasion.