I am not a football expert or an athletic recruiting one, so take all of this with a bucket of salt and consult with people who actually are experts. It does appear as though you need some suggestions of some schools from which you might build your lists. Thus, I have two different lists for you.
The first list is a series of schools (D1 & D3) that have fairly low admit rates but do have a varsity football team, but are not extraordinarily known for their sports teams (like Notre Dame). All of these schools also offer merit aid, though at some it’s extremely difficult to get it So, even if your family doesn’t qualify for need-based aid, these schools could still meet the budgeted price.
To prevent too much visual clutter, I will post the second list in a separate post.
D1
- Bucknell (PA ): About 3700 undergrads
- Colgate (NY): About 3100 undergrads
- College of the Holy Cross (MA): About 3100 undergrads
- Davidson (NC): About 1900 undergrads
- Lafayette (PA ): About 2700 undergrads
- Lehigh (PA ): About 5600 undergrads
- Northwestern (IL): About 9k undergrads; their athletics department has been having some significant issues. As they’re in the Big 10, this may be too far, but getting an academically strong quarterback while they’re in turmoil could be a reasonable option. Speaking, of course, as a total layperson.
- Rice (TX): About 4500 undergrads
- U. of Richmond (VA): About 3100 undergrads
- Villanova (PA ): About 7k undergrads
- Wake Forest (NC): About 5400 undergrads, though I think they may have actually done decently well in football last year, so may be more competitive than I at first thought.
- William & Mary (VA): About 6800 undergrads
D3
- Carnegie Mellon (PA ): About 7100 undergrads…only if you qualify for need-based aid
- Case Western (OH): About 6k undergrads
- Denison (OH): About 2300 undergrads
- Johns Hopkins (MD): About 6k undergrads
- Kenyon (OH): About 1900 undergrads
- Macalester (MN): About 2300 undergrads
- Trinity (TX): About 2500 undergrads