SMU: Zero ranked finishes in football since 1984. Zero Conference championships since 1984. Very good (#72 in US News) academically, religiously affiliated. Non-AAU R2 research university (BYU is R2). Located in Dallas but no significant following.
Rice. Zero ranked finishes in the last 60 years. Two conference championships (Co-SWC in 1994, C-USA in 2013) in the last 30 years. Elite academically (#15 in US News), private secular. AAU and R1 research university. Located in Houston but no significant following.