After buying the land, take Horadric's advice and go talk to Cory. He'll tell you he's busy and can't help. You have two options now; you can buy him off, or become his supplier and provide him with a large list of supplies. The fastest way is to pay him the 2 gold coins, and he'll build your new tavern for you in the deal.
Either way, you'll have to sleep to get the tavern built. Use some stamina, go home and sleep, and you'll wake up to an achievement.