According to the Secretary of State's website, here are the races happening this year:
District 3: Jim Scheer is running unopposed
District 4 (east Omaha): Elizabeth O'Connor (incumbent, seems to be one of the problems) vs. Jim Rogers. O'Connor has been mentioned by a couple people as generally not being helpful towards NU football, etc. Rogers is a longtime UNO guy & an academic. Seemed to be a nerdy but forward thinking guy, probably centrist politics. Analysis: Rogers would likely represent at least some improvement
District 5 (south Lancaster County: Rob Schafer (incumbent, chairman of the regents, unknown) vs. Gary Rogge & Jerome Wohleb. Schafer has been publicly supportive of UNL athletics. Politics within the BoR unknown, but seems to be the type who would at least side with the football team over academics/partisans who were hostile to sports.
Rogge shows up in various municipal government meeting notes testifying for about small issues, an op-ed complaining about Kansas farmers doing field burns, and was a candidate for an OPPD office & Lt. Governor, but never appears to have set up any web pages or info about himself. Doesn't seem like a serious candidacy. Wohleb is a pharmacy director in Lincoln. Older, no associations with sports that I can find, hasn't produced any info about himself yet. Impression is an academic type probably running for reasons related to the medical field. Analysis: Schafer seems like the best option here
District 8 (west Omaha): Barbara Weitz (incumbent, one of the bigger problems according to multiple sources) vs. Zachary Mellender. Weitz is super, super into girl's & women's stuff, especially politically leftist orgs. Likely outrightly hostile towards football, etc. Mellender is younger, does business systems stuff for the Omaha Zoo, has been on a state information technology panel appointed by the governor, and seems generally like a more analytical/logistical guy. Analysis: Mellender better by default.