The wife and I stayed at the red brick inn which is closer to downtown/gruene hall and is owned by green river inn. We booked through gruene river inn and picked up our keys there. It has been several years ago but we were going to see a show at Gruene Hall and I didn't want to drive afterwards.
It was very convenient, but is basically an old house turned B&B. It is what I imagine staying at an old persons house would be like. We basically rolled into town in the afternoon, went to the room and changed, and went out, then slept there.
I would definitely stay there again if I was going back to the area.
I do remember a 2 night minimum on weekends.
ETA, I agree with Vernada about GRI not being safe walking distance to downtown. It is probably already booked, but check out the Gruene Mansion Inn.