I'm actually from Dallas! Union Station is right in the middle of downtown. During the day it wont be an issue at all as it's a popular area, and even early in the evening you'll be fine. I'd just try to avoid walking around the downtown area super late at night. The areas to avoid are mostly south of downtown though, specifically around the Oak Cliff district. Deep Ellum is also a popular area to visit but there's been a bit of an uptick in crime lately. I still go there all the time though and don't ever have issues so there's my anecdotal take
I absolutely love Austin, and if you're on congress street you'll be just fine. More people walk around Austin compared to most other cities here so there'll be plenty to do close to where you're at regardless of which side of the river you'll be on.