Hall of Beginnings Locations:

Dragonborn - Outside Helgen (If the quest doesn't show up after a minute, talk to Hadvar)
Warrior - Jorrvaskr (Whiterun)
Mage - College of Winterhold (near Feralda)
Thief - Riften (near the market)
Alchemist - Arcadia's Cauldron
Blacksmith - Whiterun Skyforge
Hunter - Hunter's Rest (Shack)
Bard - Solitude Bards College
Beggar - Beggar's Row (Riften)
Assassin - Windhelm (Aventus Aretino's house)
Bandit - Halted Stream Camp
Skooma Dealer - Markarth Warrens
Pirate - The Red Wave
Town Guard - Whiterun (near the gate)
Noble - Solitude (Blue Palace)
Treasure Hunter - Angarvunde
Scholar - Winterhold College Arcanaeum (Will be changed later on)
Vigilant of Stendarr - Hall of the Vigilant
Necromancer - Fellglow Keep
Forsworn - Druadach Redoubt
Thalmor - Northwatch Keep
Khajiit Caravan - Random
Stronghold (Orc) - Dushnikh Yal