Seoul, Busan, Gyeongju, and even Jeju-do are well traveled, and most tour companies to South Korea will cover those areas. But South Korea is an exciting place to explore on your own, so I've provided a few itineraries, most of which don't stray too far from the major cities, to help you plan your trip.
Bear in mind that although South Korea is small in land mass, the hilly terrain and lack of major roads increase travel time between locations and attractions. Although you can rent a car, I don't suggest it unless you're planning to go well off the beaten path. The best ways to get around are by rail and by bus.
Trains in South Korea are cheap, reliable, and a comfortable way to travel. High-speed KTX trains will help you save time. Consider buying a KTX pass before you arrive, as it will save you money, too.
In general, trains will take you only to stations in major cities, but not to many temples and other remote locations. Luckily, the bus system is quite efficient and all towns have at least one bus that goes to even the most remote locations. A combination of train and bus travel will probably be your best bet.
Note: This information was accurate when it was published, but can change without notice. Please be sure to confirm all rates and details directly with the companies in question before planning your trip.