I’m familiar with the public university systems in three states, New York, New Jersey and Pennsylvania. Each of these states have at least two levels of state colleges and universities, the major research institutions, and the smaller colleges and universities which generally began their existence as teachers colleges.
New York
There is one major system of public universities in New York, the State University of New York (SUNY). The SUNY system is divided into two levels of institutions, four University Centers at Albany, Binghamton, Buffalo, and Stony Brook, and other State University Colleges around the state, including Plattsburgh, Geneseo, Purchase, Brockport, etc. The University Centers are the major research institutions and are generally more difficult to get into. The smaller colleges generally began their existence as teachers colleges, before being swept into the SUNY system and expanded.
SUNY also sponsors some, but not all, of the schools at Cornell University, including the vet school, the agriculture school, etc. Other Cornell schools are private.
There is also the City University of New York (CUNY) system, which is, I believe, financed half and half between the City of New York and SUNY. CUNY has the graduate center, which sponsors most doctoral and advanced research, and a number of undergraduate colleges, including City College of New York, Baruch College, Hunter College, Brooklyn College, Queens College, John Jay Coillege of Criminal Justice, the College of Staten Island, etc. There are also CUNY community colleges, such as Manhattan Community College, Queensboro, etc., though I believe that those are financed entirely by the City.
New Jersey
As mentioned above, New Jersey has Rutgers, the State University of New Jersey, with its main campus in New Brunswick, but with other campuses in Newark and Camden. New Jersey also has a system of smaller state colleges and universities, including Montclair State, Ramapo State, Rowan University (formerly Glassboro State), the College of New Jersey (formerly Trenton State), etc., which generally began as teachers colleges as well.
Pennsylvania
Pennsylvania has three major state-supported universities and the State System of Higher Education, a system of about a dozen smaller colleges and universities. The Pennsylvania State University, with its main campus in State College and a few branch campuses, Temple University in Philadelphia and the University of Pittsburgh are the major universities, though I think that the type of organization and level of support are different for Penn State on the one hand and Temple and Pitt on the other. The smaller universities include East Stroudsburg University, Indiana University of Pennsylvania, California University of Pennsylvania, Slippery Rock State, Shippensburg State, Cheney State, Clarion State, etc., most of which began as teachers colleges, I believe.