Yes you can get a fine music education at many state schools. I have known kids that did UG music degrees at Univ of MN, Madison and Nebraska. A good friend of my D did a BS in business and a BM in music at our state school. He looked at schools with conservatories but decide it may be tough to do both well at a high level…and money mattered. He got a very good scholarship from the business school. He found a good voice teacher at the state school and the music school was accommodating to his dual degree. State schools with good but maybe not top music programs can be a good option for dual degree students. This student is now in grad school at a conservatory. In your case you may need to look closely at the music faculty for state schools of interest. If you find a school with a good teacher you can contact the music school administration to ask questions about dual degrees. Or others on this site may have suggestions in your area or for his instrument.