Seoul is the capital of South Korea; its airport was voted most beautiful in the world in 2009. Your cheap flights to Seoul will land in that beautiful airport, Seoul Inchon International. Like most Asian airports, Seoul Inchon has luxury services that include a golf course, spa, indoor gardens, and even a casino. To get to the city, you can take the Express Railway or a public bus. Taxis are available as are rental cars. If you take a taxi, be aware that most drivers do not speak English so you will want to have your destination written down in Korean. Rental car kiosks include Avis, Hertz, and Khumbo and are located at arrivals.
Flights to Seoul are to a densely populated country that experiences the bane of traffic like most other densely populated cities. So while a car is possible, it is not recommended. Likewise, taking taxis can become very expensive due to the dense traffic increasing the travel time. It's better to walk if you can. If you can't, there is excellent public transportation: bus routes and the subway. Most signs are in Korean and in English. Better still, if you can, hire a guide to help you get around.
This was formerly a royal city and here are at least five different palaces open to the public. One of the most impressive is Gyeongbok-gung where television dramas are filmed. It also houses the Joseon Palace Museum and the Korean Folk Museum. Surrounded by mountains, there is excellent hiking available at all levels of fitness and expertise. Bukhansan is the most popular and Gwanaksan is the location of the Sammak Temple. The Olympic Park is still open and there are other parks throughout Seoul. The N Seoul, Namsan Tower is the largest tower in Asia and offers spectacular views.
You will be happy with the Seoul flights; as a major city, Seoul has plenty of shopping - it just depends on what you want to buy. Namdaemun is the largest open air market. You can buy clothing, food, and electronics. Dongdaemun is a more modern shopping facility which includes many indoor shops. Apgujeong is the place to go for designer goods. You'll be glad you saved money on cheap airfare to Seoul, Korea so you'll have more to spend here. When you're hungry you'll find that there is no shortage of restaurants from cheap to expensive. Ala-too Cafe offers a wide range of choices from Russian to Central Asian. The Frypan serves American style food. There are countless bars and clubs as well as shows and performances.