Tears of the Savior
Quest From: S'drassa;
S'drassa, Mages Guild alchemist in Leyawiin will ask you to find rare crystals known as Garridan's Tears for him. You'll have to talk to Julienne Fanis in Arcane University for some more detail on their location. She'll tell you to find a book called Knightfall. It can be bought in The First Edition in Market District. After reading the book, a new map marker will be added. In order to get there, you'll need Refined Frost Salts - you can buy them from Julienne.
Go to Frostfire Cave. Use enchanted door (screenshot above) and you'll find yourself in Garridan's chamber. There's a Frost Atronach here, together with 5 barely visible crystals. Use the map below to find them. Be quick about it, as the frost in this room impacts your health. Go back to S'drassa to get your reward.
Whom Gods Annoy
Quest From: Rosentia Gallenus;
When talking to Leyawiin townsfolk you'll eventually hear about strange noises and smells coming out of Rosentia Gallenus' house. Go there and break in. Inside you'll meet Rosentia herself and a few scamps. Talk to Rosentia to find out that these creatures are here because of cursed staff she recently bought. Go to Alves Uvenim in local Mages Guild.
It turns out that the only way for Rosentia to get rid of the staff is if somebody accepted it willingly. Agree to that and go to Darkfathom Cave east of the city. The cave is a small dungeon filled with daedric monsters. When you reach the altar in the eastern part of the map, drop the staff and leave. You'll get Ring of Eidolon's Edge as your reward from Rosentia.
HINT: When you possess the staff, Everscamps that follow you are good training assistants. Just practice your battle skills on them if you like.
Mazoga the Orc
Quest From: Count Marius Caro;
In Leyawiin castle there's an Orc named Mazoga. Talk to the Count about her, he'll ask you to try and solve the problem. Talk to Mazoga herself to find out she wants to speak to Weebam-Na. Find him in Leyawiin and escort to the castle. You might have to raise his disposition in order for him to agree.
Mazoga wants to go to Fisherman's Rock north of the city, but Weebam-Na won't go with her. Tell her that you will accompany her and do so. Once you're in there, Mazoga will start a conversation with some bandits. Assist her when the fight breaks out. When they're all dead, go back to the Count.
Knights of the While Stallion
Quest From: Count Marius Caro;
The Count will promise you a title of Knight-Errand if you kill a bandit named Brugo. Mazoga knows that he's hiding in Telepe, west of Leyawiin. Head there overnight.
Ruins are not well guarded, apart from Brugo there will be some low-level bandits. By the leader's body you'll find a key that'll allow you to open the chest in (C). To get to it, past the gate at (B) you'll have to press the button at (A).
The grateful Count will grant a knight title to both you and Mazoga. You'll get a key to White Stallion Lodge, north of the city, and a cool Leyawiin Shield.
Raid on Greyland
Quest From: Lerexus Callidus;
Outside the north gate of the city, you'll meet Lerexus Callidus, who is after a drug dealing gang. He'll tell you to go to Greyland and kill Kylius Lonavo.
Easy as it gets - just enter the house and do your thing. Nobody will bother you with any alternative solutions to this quest. Take the ring from Kylius body and show it to Lerexus for some gold.