Where New Meets Old
South Korea can be a very fascinating country to visit. It has very modern infrastructure and technology, but it is possible to still catch glimpses of old world traditions that have been passed down from generation to generation. If you're creative with you destinations and accommodation choices, you may find yourself in some unique situations. Consider doing a homestay, or staying in a minbak. Found mainly in rural areas, this unique experience allows you to rent a room in a local's home. They're quite common and popular near national parks. They can range dramatically in quality and price, with some being surprisingly fancy and high end. Typically you will get a TV in your room and you will share a bathroom. If you do choose a fancier option you may have a bathroom that accompanies your room, but these are rare and harder to come by.
Something For Everyone
South Korea has a wide range of options for both budget travelers and luxury travelers, as well as everybody in between. Seoul is probably the most expensive area in South Korea, and you can expect to pay roughly twice as much for accommodation in this city as you would elsewhere in South Korea. As such, it will dramatically help your budget to head to the countryside and see more of South Korea than just its capital city. This will also give you a more diverse trip and will prove quite enjoyable as well.
There are budget accommodation choices, but hostels are not as common in South Korea as they are elsewhere in Asia or Europe. There is a unique option that you might consider, referred to as a jimjilbang. It is a public bathhouse that is usually affordable, but is quite simple and offers little more than a place to sleep and a shower.
Traditional Homes or Cheap Motels
There are some great options for accommodation in South Korea that allow you to truly experience the unique culture in this country. In the countryside, minbaks, or homestays are the best option to experience a traditional home and interact with a local family for an affordable price. If you're in the cities, hostels are likely limited, but you will find motels. Keep in mind that motels are more like Japan's "love hotels" and less like western style motels. They often cater to young couples looking for an "escape". You will also find full service hotels that can be quite expensive. There are some cheaper options around so do some research ahead of time.
Jogye, Korea's largest Buddhist sect, operates the Temple Stay program, which lets you stay at a temple for a day. You are expected to work and wake up early to participate in prayers. A donation is typically expected as well, but this can be a very rewarding experience.
As previously mentioned, Seoul is probably the most expensive city in South Korea with prices usually about twice as much as they are in other parts of the country. There are some hostels available, but not nearly as many as you might find in other Asian cities. The most popular districts with backpackers are either Jongno, in the northeast part of the city, or Hongdae, Sinchon which is to the west. Jongno is just a short walk from Dongdaemun Market and it is best located for sightseeing. It's conveniently close to many different attractions and it's in a vibrant neighborhood. It's also easily accessible from Incheon Airport by public bus, although the trip can take upwards of and hour and a half. The Hongdae, Sinchon area is in a university area so it is surrounded by activities geared toward a younger crowd. There are also many affordable restaurants, bars and cafes nearby so it's a great place to stay if you're looking for cheap entertainment. There is a public bus that makes the trip from this area to the Incheon Airport in about an hours time.
Pusan is another popular destination in South Korea. It has some affordable accommodation options but you'll find a greater selection and a higher quality if you're willing to spend a little more. Many budget travelers choose to stay in a Love Motel, of which there are many in the city. There is a high concentration around the bus terminals, and these are perhaps the best deal in town.
There are a few good hostels around the city as well. Many offer interesting amenities including Korean lessons, cooking classes, or tours so inquire about what options might be available to you.
Mid-range options are more limited so it is advised that you make reservations in advance if this is what you are looking for. The higher end options tend to be more concentrated along Haeundae Beach. You can choose between either an ocean view room or a city view room, but expect to pay more for an ocean few. Rates are also higher on weekends and during the peak summer months, specifically July and August. Also make sure there is not a special event going on as this will inflate the prices as well. If you're looking for the best deal head to the area on a week day during the low season.