I'm not much for IPAs either. I do like sours, but understand why a lot of folks don't.
My favorite styles are European and nobody in the US does European styles better than Live Oak. It's out of the way, out by the airport, but has a really nice biergarten. Their Pilz, Hefeweizen, and Big Bark Vienna-style lagers are all excellent. They also do a lot of smoked beer styles but it sounds like that might be a bit outside your comfort zone. Still, you could try one and see.
And Celis is still quite good with their classic Belgian style beers.
And I like some of the beers at Pinthouse Pizza, they have a a couple of traditional stouts and lagers that are tasty, along with quite a few IPAs. And although I'm no IPA-lover, the juicy/New England styles can be good, and Pinthouse's Electric Jellyfish falls into that category for me.
Many of the other widely praised local Austin breweries tend toward the hoppier IPAs and/or sours.