How about it hounds and beer snobs, any old time Biergarten's your keeping a secret? I Googled up Houston + Biergarten and got two hits locally. One was in the Village area, the other out on Harrisburg.
If the one on Harrisburg is the one I'm thinking of, it's woefully miscategorized.
GingerMan in the Rice Village probably qualifies, as would Hans Bier Haus close by.
Place that you can sit outside with decent beer selections: Petrol Station and Onion Creek.
The Flying Saucer probably has the best beer selection in town, but no outdoor seating and it's LOUD LOUD LOUD. I kinda hate going there.
Anvil has about a dozen great beers on tap, but no outdoor seating.
Those are the few that immediately came to mind.