The suit will be tossed out. Businesses can serve whomever they want to serve as long as they comply with any applicable laws regarding discrimination on the basis of religion, race or ethnicity. There's nothing in any law of which I'm aware that would add geography to that list.
This isn't true. There are specifically protected categories that discriminating on the basis of is always unlawful - as you said, those are religion, race, color, and national origin.
However, in a place of public accommodation like a stadium, arena, or restaurant, it is also unlawful to refuse service based on arbitrary discrimination that serves no legitimate business purpose. This is because places of public accommodation are subject to equal protection laws due to the nature of the product or service being provided (contrast this to a nightclub, which can legally discriminate arbitrarily so long as it is not discriminating on the basis of race, color, national origin, or religion).
For example, the Seahawks could not lawfully choose to sell tickets only to men even though sex and gender are not specifically protected categories because that would be an arbitrary refusal of service to women with no legitimate business rationale.
However, I think discriminating in ticket sales based on geography serves a legitimate business purpose for the home team, since a friendly crowd helps a team and victories increase a team's revenue potential.
It's definitely a more complicated legal issue than it seems on its face, and a good Constitutional attorney could put up a good case as to why it was arbitrary refusal of service, but I just don't think the case is as strong as the case for it being a legitimate business reason.