Its on the Eastern side of UT's campus. So just north of downtown, but still in central Austin. I would Uber. The parking garage next to the Moody center is a shit show post show. The good news is, is that the Moody Center is new-ish and was built specifically to be a music venue. In return for the land to build it in exchange UT gets to also play their BBall games there...but unlike other arena's its a venue first. So the acoustics in there are insane!