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You can do the Vlastarus quests each day to get the boxes free
Also, if you park your characters in one of the shops there they will not be returned to your Alliance gate starting point, and you can log them in right back where they were.
There are 16 dailies per capturable town and each rewards a set piece of one of the types associated with that town (light, heavy or medium armor sets + associated jewelry and weapons).
Bruma (Medium)
Barkskin
Crusader
Eagle Eye
Hawk's Eye
Kyne's Kiss
Sentry
Shadow Walker
Shield of the Valiant
The Morag Tong
Twin Sisters
Vengeance Leech
Ward of Cyrodiil
Cropsford (Light)
Almalexia's Mercy
Buffer of the Swift
Curse Eater
Desert Rose
Grace of the Ancients
Light of Cyrodiil
Noble Duelist's Silks
Prayer Shawl
Robes of Alteration Mastery
Robes of Onslaught
The Arch-Mage
Wrath of the Imperium
Vlastarus (Heavy)
Affliction Item
Alessian Order
Armor of the Truth
Bastion of the Heartland
Beckoning Steel
Blessing of the Potentates
Crest of Cyrodiil
Deadly Strike
Durok's Bane
Elf Bane
Ravager
Sergeant's Mail
The Juggernaut
You don't need to capture the town to obtain nor turn in the quests, though it certainly makes it easier.
Each of the quests is a simply "go fetch something/kill someone" type and a couple will take you into delves. There's 2 NPCs that give out quests so you can have two active at a time, though as often as not they send you in opposite directions anyway.