Some of the schools from the link I included above that you may want to take a closer look at include (with their percentage of need met):
Loyola Maryland: 91%
Lawrence (WI): 94%
College of Wooster (OH): 93%
Luther (IA): 94%
Wheaton (MA): 91%
Knox (IL): 93%
Valparaiso (IN): 95%
Berea (KY): 96%
Berea is a work college which is only for a certain type of student, but if it’s right for your daughter, it should certainly be in consideration. There were also some Minnesota schools that could be considered, but as you indicated your daughter was hoping to go out-of-state, all of these schools are.