SSO is tangentally correct, but I want to add some context as well.
For Starters: Host sites for the entire tournament (First Round through Final Four) are determined by the NCAA in advance, with us knowing currently where the Final Four will be through 2030 and First/Second rounds through 2026. Link to site list
here.
Each first round site hosts essentially 2 separate “pods“ of 4 teams leading to 6 total games (4 in the first round 2 in the second round) in that site. See CBS Bracketology link
here for the sites as an example. Sites do not host pre-determined seed line matchups, they are “chosen” by highly ranked/low seeded geographically proximate teams. This means the seed lines for each first round site changes depending on the geographic proximity of the higher rated teams to the host sites.
Selection: For the first rounds, the NCAA will select host sites across the country to provide a variety of locales for qualifying teams to play in. For the first weekend, the NCAA provides the lower seeded teams a choice of their most preferential site so that they don’t have to travel overly far from their home location as a rule of thumb. The NCAA Selection Committee will select the qualifying teams for the tournament and then seed every team in the field from 1-68. The lower the seed you are, the more geographical preference you are given (I.e. UConn as a 1 will choose to play in Brooklyn due to proximity, and all else being equal, 1 or 2 seed UNC will choose Charlotte).
The main reason you‘d likely not see Nebraska in Omaha is so as to not give an “unfair” advantage to the higher seed against a lower seed in the first/second rounds. As an example of this, the year South Carolina men went to the Final Four (2017), they were a 7 seed, playing 2 seed Duke in Greenville, SC which is like 60 mins from their campus in Columbia, SC. This of course caused a ruckus and a spotlight to be shined on this issue due to its “unfairness” to the lower rated seed where Duke basically played a road game at South Carolina despite being a top 8 seed in the tournament.
Of course, it is harder and harder to avoid geographical conflicts of interest the further down the seed line you get due to their being more teams already slotted in the bracket and each of them having their own geographical preferences and proximity to the host sites. So while it is entirely possible that Nebraska gets put in Omaha, it will depend on who else qualifies for the tournament and is in their same general seed line to determine which side they ultimately wind up in.
Lastly, but interesting, teams can’t play at a “home” gym in the first round, so a team like Pickle Smoochers could never play in Omaha in the first round even if they were the #1 overall seed this year with Omaha as an option to them because they play more than x% of their games per year at that gym.
TLDR: Sites depend on seeding, with geographical preference given to higher seeds to choose sites that are closer to their campus to minimize travel and maximize fan support while not putting the “best” teams at a disadvantage