There are only three buildings in Dorngas you really need to know about, since the rest are houses and barracks for the soldiers.
Upon entering through the South Gate the building immediately to the west contains two shops. The southern shop is a common provisioner, and the northern shop is actually a library of sorts, run by Wray the sage. Wray will identify your items for a fairly hefty fee, but more importantly he has a lot of information about the quarantine of Valorim, the attack of Footracer by Alien Beasts, Blackcrag fortress, etc. Get all the information you can from him.
Just to the east of the North Gate is a common fletcher, and east of that is the inn. The inn is run by Radewitz, who also sells maps of Footracer Province. The other thing of note in the inn is in the northwestern room. Standing in the corner you'll find Zik, who's the object of the quest for the mayor of Softport. Talk to him until he attacks you, and then kill him. Once he's dead don't forget to return to Softport to get your reward.