There’s free parking at the Public Safety Department across the street from Rice-Eccles and take the shuttle that drops you off right at the arena. That’s what I’ve been doing the last couple of years.
For future reference, there’s also parking and a shuttle at the Eccles Broadcast building (southeast of the softball field.) Honestly, given the limited amount of parking that is available on campus, I think the U actually does a pretty good job between the shuttle service and Trax.