My dad is a musician in Branson, and I'm a former resident.
Silver Dollar City is second only to WDW in terms of theme in my opinion. I have spent more time there than I could even calculate, and it never gets old for me. It is so fun! But there are hills, hills, hills, so be prepared for that while walking!
There's tons of mini golf and go carts, wax museum, Ripley's Believe it or Not, the Landing for shopping/dining, ziplines, two lakes, etc... Visit Dick's 5 and 10 if you go downtown near the landing. It's a fun store!
There's also the Tanger outlet mall. I worked at the
Disney Store there
There's also an Imax theater, which is a family favorite.
While I have never been to the National Tiger Sanctuary, we do love Turpentine Creek in Eureka Springs, AR, which is about an hour away. In fact, Eureka Springs is an awesome destination, too, depending on how much time you have!
I don't view Branson the way many people do, because it has always been part of my life in a "real world" way vs. just a tourist destination, but it still has a lot to offer!
Oh, and go get some Andy's Frozen Custard if you don't have one near where you live!
editing to add...White Water is there if you're going in summer!