Some big merit-for-stats schools are listed here:
Automatic Full Tuition / Full Ride Scholarships
That thread also has a link to a thread about large merit scholarships guaranteed for National Merit Finalists (or sometimes Semifinalists).
Need based aid is often best found at in-state publics and highly selective privates. Check the net price calculator at each school's web site, but note that if your family situation is more complex than what it asks about, it may not be as accurate as for those with "more common" situations.