Once your balance is more than a convenience store can handle, head to a customer service center inside a subway station in the Seoul metropolitan area. They handle regular balance refunds, and they're also one of only two places (T-money Town is the other) that offer partial refunds — taking out a set amount between 10,000 and 50,000 won, in 10,000 won steps, instead of emptying the card.
If your balance is over 50,000 won, T-money's guidance points you to T-money Town, the company's own service center, or a bank ATM with T-money refund service linked to an account in your name. T-money Town can refund up to 500,000 won per person per day, and asks for ID (name, birth date, contact) on refunds of 50,000 won or more. The bank ATM route is generally more useful if you already have a Korean bank account than for a short visit.
One thing to know before you go: a refund of 100,000 won or more at T-money Town isn't paid in cash on the spot. The balance comes off your card that day, and the money is transferred to a bank account after 6 p.m. the next business day. You'll need to bring ID and a copy of your bankbook.
If you don't have a Korean bank account, check with T-money before you visit so you know what will work for you.