Mokpo has several official tourist information centers, so use the one closest to the transport hub or attraction you are already at rather than crossing the city for help.
If you arrive by train, Mokpo Station Tourist Information Center is on the first floor of Mokpo Station and the city currently lists it as open 09:00–18:00. If you arrive by long-distance bus, the Bus Terminal Tourist Information Center is on the first floor of Mokpo Central Bus Terminal and is also listed at 09:00–18:00.
For international-ferry passengers, the International Passenger Terminal Tourist Information Center is on the first floor at 148 Haean-ro 14 and has a different schedule: the city currently lists 18:30–23:00 and says it is closed on Saturdays and Sundays. Do not assume the station and ferry desks keep the same hours.
Mokpo also lists the General Tourist Information Center, Peace Plaza, Nojeokbong and Gatbawi information centers, generally at 09:00–18:00 on the current English city page. The same page lists service languages as English, Japanese and Chinese.
Practical next step: save the phone number for the desk matching your arrival point, and recheck the city page on a holiday or before a late arrival because staffing and opening hours can change.