Wwwwweeeeeellllllllllll.... Before you go and cancel your trip down to old-folk-ville, I would like to try and counter my right honorable fella's before me that so kindly spoke of Branson. I currently live here in the little ozark town known for it's small production show business and not so glamorous amenities. I've been here for 3 yrs now and I will admit, we are a little behind on the craft brew movement (I mean c'mon it only started, what, 30 yrs ago? This is the ozarks! lol.). However, since I have been here we have made some improvements. Not so much in the way of Microbreweries but definitely in the selection of beer in restaurants. Let me give you a few options.
The only microbrewery in town pretty much keeps it a secret to itself and I can see why. The folks at a restaurant called "Charlies Ribs" has two brews in house. Mediocre at best for our standards here on the homebrewtalk but a microbrew nonetheless.
A few restaurants have been doing their best to broaden the horizon here in Branson. Probably the two favorites are Old Chicago and Waxy O'Shea's, both located at the Branson Landing.
One last resort would be the only "liquor store" in town. Missouri has some of the most loose regulations on alcohol next to Nevada and Louisiana, so hard liquor and everything below can be found at any retail place around (not kidding, go to walgreens and buy a fith). However, because of that "wonderful" comodity, it is very hard to find much of a selection in specialty beers. So with that in mind I recommend "The Wine Company" for your harder to find beers. This you can take back to your hotel or condo.
I hope this helps you out. Someday I would like to open a legitimate brewhaus here in Branson. I have the place picked out and everything. But if you guys keep running off my potential customers, what hopes do I have? =P