Jebudo is an island in the West Sea in Seoshin-myeon, technically within the city limits of Hwaseong. It measures around one square kilometer with 12 km of coastline, and though nobody really makes it their residence it's fairly popular as a travel spot since 2000.
The rather crude concrete bridge leading to the island is underwater half the day, so traffic back and forth is allowed only twice a day: in the morning, from 7:00 am until 11:30 am, and in the evening from 6:40 pm until 1:00 am. The bridge doesn't have pedestrian paths or streetlights, but you can make the approximately 15-minute trek if you stick to the sides and are careful. If you'd rather not walk, the Jebudo Bus (1,000 won fare) runs from the bus stop next to the Waikiki Spa to several points on the island, including the police station and the amusement park near the beach.
The easiest way to get there is to take 330 intercity bus, which goes right to the bus stop just yards from the bridge to the island. From Suwon Station, where the 330 doesn't stop, take the 400, 400-1, 490, or 499 bus and change to the 330 at the Seoshin bus terminal. If you opt to drive there, be prepared to wait in a very long line for the bridge to open.
There are hotels on both the island and the mainland, mostly minbaks and pensions, though there are a few more conventional hotels, such as the Hill House Hotel and the Jebu Tourist Hotel, which are also the most expensive choice (they'll ask westerners for 50,000 a room). Probably the cheapest place to stay is the Waikiki Spa's jjimjilbang on the mainland.
Nearly all the restaurants on both the mainland and the island serve up the same menu -- grilled shellfish and kalguksu. There is a tiny kimbap and jjajang shack near the amusement park, and a few other restaurants here and there serve up naengmyeon. On the mainland is the Mayflower restaurant, housed in what used to be a large sailboat.
The beach can be a nice place to take a stroll, or shoot off fireworks at night. The fireworks are available at the convenience store next to the amusement park. The amusement park has a few rides, a "disco" dance floor, and some dirt bikes you can ride around on. There are also some hiking trails, and a jjimjilbang in the Waikiki Spa on the mainland. There are no bars or clubs.