I found a new (to me) brand that I quite like and recommend. It's called Dr. Tima Honey Root Beer. It is honey-sweetened, no high-fructose corn syrup. All natural ingredients, in fact, the ingredient list is as follows: purified carbonated water, honey, oil of wintergreen, vanilla, oil of sweet birch, anice, cloves, yucca plant extract, and fruit juices. No idea what the yucca plant extract is or is for. ;-) And, like most root beers, it has no caffeine.
You're more likely to find it in a good health food or organic grocery store. I found it at a coop in Las Cruces over the weekend, it isn't cheap at a dollar a bottle, but it is pretty good. It's a little different taste than conventional root beers, and the honey is kind of subtle. Unfortunately I can't easily find a web site for the maker.