The Greenwood County Hospital group is a critical-access, not-for-profit medical group comprised of: Greenwood County Hospital. 100 W. 16th St., Eureka, KS 67045. (620) 583-7451. Eureka Clinic. East End of the Hospital. (620) 583-5274. Howard Clinic. 118 Wabash, Howard, KS 67350..