I walked into Gruene Hall early on a Sunday morning. The young lady behind the bar was the only person there. However, I was only taking photos of the interior. I did have a big camera and tripod. I reckon it will depend on the person behind the bar at the moment.
There is a nice open grassy area next to Gruene Hall and under the watertower. Benches, etc. for your friends. Mr. Gruene's Office would make a nice backdrop. Big tree in the front yard. nobody will bother you there.
Gruene Hall, Sunday, 10am. Not too busy.
Mr. Gruene's Office, Saturday, 2 pm. Gruene was full of folks, traffic, etc. Fortunately all of that was behind me.
I suggest you get there early. Like 7am-8am. When will you be going? Check the Gruene Events schedule in the internet. Find out if the town will be full for a festival or something like that.