Dixie National Forest — the largest national forest in the state (1,900,000 acres!) is mostly high altitude evergreen forest, with lots of hunting, fishing, camping, hiking, climbing, and even spelunking possibilities
Zion National Park — one of America's most popular parks is breathtaking and has lots of excellent hikes ranging from very easy to very challenging, but all of them rewarding
The part of Utah known as Dixie is the southwestern corner of the state. It bears this incongruous name (more commonly associated with the South region of the United States, far to the southeast of Utah) because early settlers were successful in practicing some of the same agriculture as in the southeastern United States. Historically it has been sparsely populated, but the growing popularity of St. George as both a retirement community and a jumping-off point for outdoor recreation is increasing the population rapidly.
Cedar City would never consider itself to be part of Dixie, it pretty much starts at the county line.