The Country building with the big guitar on it has good mini golf. Also last time we were in Branson we went to a new mini golf area. I can't remember the name of it. It was themed with dinosaurs. I do remember that it had a big volcano right in the middle of it. It was really cool.
We don't really go to museums although everytime we go to Branson my dad always says, "Man, I really want to go to that Veterans Museum sometime. I'll drop you guys off at Silver Dollar City for the day and I'll just go there!" To this date we have never been. I don't know if it's a Veterans Museum or a specific war museum though. Sorry, I can never remember the names of these places!
I've also wanted to go to the new Titanic museum (it's not really museum but I think it could be classified as one). It looks really interesting (from the outside anyways).
For shopping we go to the Tanger Outlets. We used to go to the Red Mall next to White Water until it kind of got run down a little bit. There are many shopping opportunities in Branson though.