Many of the best football teams are not great basketball schools, but here is my list so far.
Army or Navy? (looks good to have an armed forces school in the mix)
Boise
BYU
Cincinnati
Houston
Memphis?
Temple?
SMU?
UCF
Uconn (for the basketball)?
USF
Utah St? (not traditionally good enough, but good enough this year for sure).
Not sure a lot of these schools could afford to be in this conference with how spread out the schools would be.