Anyone knows if there's badminton in Cheon An??

Of course!

There is badminton everywhere in Korea. In fact, Cheonan hosted a nationwide amateur tournament last year. Badmintontimes lists 11 Cheonan clubs. I don't know if that link pulls up the right page for you.

There seem to be 3 clubs in Ssangyong-dong, which, if I'm not mistaken, is visible from Cheonan train station (not KTX). There is a gym at the southern campus of Seoul Nat'l University that has 9 courts and costs 30,000won a month. That is likely well outside of the city proper, though (yes, I just checked: it's 2.5km from Sunghwan Station - not named after Park Sunghwan)

Either tell me your general location or see if you can make sense of the list or find a colleague/classmate/etc. who can help you find a club near you.

I'd invite you to play up here in Suwon but that would be over an hour on the commuter train. Best to find something local.

Cheonan appears to have a dedicated badminton gym with 6 courts. It's in Cheongdang-dong and seems to be ruled by the Cheonan Badminton Club.

 

There is a club listed for the main sports complex. It says the gym is in the basement of the Yoo Gwan Soon Gymnasium and that it has 7 courts. Does that sound like the place you visited? Unfortunately, the Yoo Gwan Soon club is the only one on the list that doesn't say anything about membership fees. There is a cell number there but the link to their website goes nowhere and who knows whether the phone owner is still in charge or even in the club. It is not unheard of for there to be a gym with no admission fee. There are several such facilities in Suwon but most are severely flawed in one or more ways (ie. no washroom, low roof, dirt floor, tent roof, etc.). There are also publicly-run facilities that charge a small admission fee(1000-1500 unless you're in Seoul). All such facilities, free to use or not, will have clubs, which often simply operate as drinking cliques. In other words, if you join their club, your 10,000 won a month gives you a monthly evening of meat and all the soju you can drink. If you don't join, you are the last resort for setting up games unless you are an ace or can find 3 other outsiders to play with you. I'm exaggerating, of course.

If I'm not mistaken, Yawoori is a shopping complex beside the bus terminal and Buldang-dong is just south of City Hall and the Sports Complex. That's quite an area in between. The three clubs at elementary schools are likely the most convenient for you and if you like the people and can stand the gym, it might be worth paying for the membership.

The closest is likely the Bongseo (since changed to Yeolliji?) Club(#8 on the list). They play at Bongseo Elementary School. Print out one of the maplets at their website and show it to a taxi driver. They apparently have 4 courts and they want a 100,000won initiation fee and then 15,000 a month. I am sure shuttles are not included.

There are also clubs at Wolbong and Ssangyong Elementary schools, which aren't far from Buldang-dong. The former (#10) is also 4 courts and more expensive than Bongseo. The Ssangyong Club has no initiation fee and is only 15,000 a month. That's a bargain. They play from 6 to 11 every evening, they say. To get there, go south from the east side of the Sports Complex (keeping the mountain on your left and City Hall on your right) and go as far as you can(just under 2km), then turn left and go about one kilometre. The school is on the left, just before the 700 series of the Ssangyong Jugong apartment complex.

To get to the other school, Bongseo, go west from Yawoori, toward the sports complex. Turn left at the road that goes south, hugging the east side of the "mountain" (Bongseo-san). After going south about 600m, the road should jog to the left and the school is right near that corner.

If the club scene with the membership fees doesn't suit you, you can try the dedicated badminton gym but it is about 6km from Yawoori and directions could be tricky but I'll try...next time.