In Yeosu, there are a couple of bars in Yeoseo-dong (the new downtown area of town, not too far from the bus terminal). One that is popular with expats is the cafe/restaurant/bar Yellow Monkey, 229-6 Yeoseo-dong (tel. 061/653-6633). There are a number of bars, hofs (German-style beer bars), and noraebang. Another bar popular with expats is the more upscale, franchise beer joint Wa Bar (tel. 061/654-2229), just a block away with a newer location in Hak-dong (tel. 061/682-0281).
In Suncheon, there are a couple of places popular with English speakers, including Elvis, 1593-4 Jorye-dong (on the second floor), and Julianna's, a Western restaurant/bar (where you can get burgers and chicken wings) in Yeonhyang-dong (Suncheon's new downtown area).
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.