Upon first entering Moon from the south the first building to the west is the inn, which is run by Lumok. If you buy some bourbon she'll talk a little bit about Blackcrag Fortress. If you ask about the town she'll tell you that there's someone named Zang in the town somewhere.
Zang can be found in an apartment in the southeast corner of town, and is the object of the quest from Starcap of Shamirik, and he'll also sell you some experience for 5000 coins, but the higher your level the lower the amount of experience gained. At higher levels it's not really worth the coins, but at lower levels it's usually worth the cost. Kill Zang once you've boughten what you want off him, and don't forget to return to Shamirik to get your reward.
North of the inn is a Common Provisioner, and northeast of that is a house.
East of the Provisioner is the Moon Library, which is run by Cerulian. Cerulian does some item identification, and also sells access to the library for 4000 coins. Cerulian will give you a quest to find the Grimoire of Then, which she believes is in Blackcrag Fortress.
Pay for admission to the library and go check out the bookshelves at the north end of the room. They teach the Protection Brew recipe and quite a few level 2 Mage spells, as well as a couple level 2 Priest spells.
The tome on a stand near the northeast corner teaches Divine Host Lv.3, but only after you've completed the Grimoire of Then quest for Cerulian.