The tuition for my university (state school) is about $7,000 per year which is coincidentally close to the maximum you can receive through the pell grant.
There’s at least one site showing (oddly enough) private schools with lower tuition than Penn State as well as some non-private [1], but you’re still over the max of a Pell grant
1: https://www.bestvalueschools.org/cheapest-colleges-in-pennsy...