Also, do apply to even more expensive private institutions. So do not rule them out because of cost. I have been amazed how much aid is available at private colleges. (Not talking Ivy League here!) My DD will be going to a small private school for about the price of our sons state school. She did not want to go to a large school like her brother or older sis. We are doing an appeal now for DD so hope to get a even more.
If your child has exceptional grades and scores, etc they may qualify for a full ride somewhere. We know two young ladies who were both offered full rides to small liberal arts schools! We didn’t realize that with our first child and wish we had. Good luck.