LGA-DTW-SFO-IAH-SEA-ANC-MSP-LAX-HNL is the longest US MR I've ever done without leaving the airport. I think it took 40 hours, but I'm not sure.
For a midnight to midnight 24 hour period, you'd want to start by going west right after midnight, turn around, come back east, and go back west. Technically you'd have 27 hours to do it in, so I guess that's cheating, but since there are no rules, who cares?
Ideally, you'd want to do this MIA-SEA for added miles...