All universities which do not have PhD programs focus mostly on teaching. Public universities like the branch campuses of U Wisconsin or U Minnesota, and many other public universities. Private universities like DePaul or Loyola in Chicago also focus on undergraduate education, as do most specialized schools like Juilliard.
Research universities, as their names imply, focus mostly on research. While many of them, especially private universities like the Ivies, will claim otherwise, it is not really true. Big research results bring in more fame and fortune than teaching awards. Public universities cannot get away with hiring big name in the field as adornments for the departments the way private universities can, and state universities are still beholden to the residents of the state.
On the other hand, though, private universities are beholden to donors, many who are parents and alumni, who mainly think of these universities as teaching institutes, rather than research institutes. Since a few individuals can have a lot of influence, it is easier to pressure private universities to invest more in teaching.
To get tenure a faculty member at any research university needs to have a stellar research record, a stellar service record, and a passable teaching record. Famous people are hired for their research record, not for their teaching abilities, and having a Nobel prize winner as the instructor of record my be cool, but if they are bad teachers their awards won’t help a student learn the material. It is important to note that professors don’t get Nobel prizes for being great teachers.