A couple have mentioned the NIT 3rd Round/Quarterfinals win over TCU. I didn't get to go to a whole lot of games as a kid and was off to college the next year and have been out-of-state since then, but I went to that game with my older brother. I think he was in law school at UNL at the time.
The atmosphere was great - I primarily remember Stan Cloudy from the team and the red, white and blue ball used in the NIT. After the game was over, they blasted 'New York, New York' through the sound system. It was awesome.