I haven't been to Big Cedar Lodge but by checking on it I found out that it's only 10 minutes from Branson. There's a lot to do in Branson but you'll need to check on things. They used to close things down some in the winter but I don't know if they still do that or not.
I recommend the Promise. It's a play about Jesus and it's awesome!! Also, there's a new play this year called Noah's Ark. Again, it's awesome!! If you check on-line you'll be able to reserve your tickets and make sure that they're open.
There are so many things to do and people to see! There's a Titanic museum that has some actual artifacts and lot of pictures. I enjoyed that.
There's Jim Stafford, Shoji Tabuchi (I've heard that this is an excellent show but we've never been), Dixie Stampede, and so much more.
Here's a site with a few of the shows. There's even more than is listed here.
http://www.bransonshows.com/showByYear.cfm?tabType=0
If you have any questions don't hesitate to ask!