Hans Bier Haus... over in West U. It's on Kirby south of Bissonnet... at Banks or Times or some such... or at least it used to be.
They also have a couple of Bocce Ball courts. We used to play Trivial Pursuit Bocce there.... you could only roll if you anwered the question correctly.
I second Han's. Also, the West Alabama Ice House is also a great place for outdoor drinking. While not technically a beer garden, it has great people watching and free hot dogs on Fridays.