University of Louisville & University of Kentucky are the first ones that come to mind. You may want to ask each individual school whether they have a waiting list, how long it the wait is, and what their rating score cut offs on entrance exams are.
Western Kentucky University offers one. They do not have a waiting list. They refresh applications into their nursing program every fall and spring semester. If you think you might have a problem getting into the university you can start taking classes at thier community college they have near campus and usually after taking classes for a semester there you can move to the university.
Have you checked the KY BON website? I don't know about KY specifically, but most state BON websites include a list of all the approved nursing education programs in the state, usually broken down by type (BSN, ADN, Diploma, LPN). That would give you a complete list of all the BSN programs in the state.
I'm guessing EKU is considered a public school..it offers the traditonal BSN program and requires you to have a 2.5 GPA (although the cut off GPA is typically around a 3.0) and you need to take pre-reqs such as Anatomy, Physiology, Chemistry, Micro, 3 pre-nursing classes, etc and have a C or better in all of those. It is not necessarily "hard" to get into but you must meet all the requirements.