There is no shortage of Korean restaurants that serve locally grown vegetables in the area. If you want something other than rice, though, your pickings are pretty slim. There are a handful of American-style fast-food restaurants in downtown Yeongju-si (the likes of Domino's Pizza and Lotteria hamburgers), but you'll find more Korean joints.
The places around Buseoksa, such as Pusoeksa Shikdang (tel. 054/633-3317) or Myeongseong Shikdang (tel. 054/633-3262), specialize in sanchae bibimbap.
The restaurants in the Sosu Seowon area specialize in traditional Korean food. A good one to try is the Cheongdari Old House (tel. 054/633-4288), where you can get a meal with vegetables usually prepared for traditional rituals.
Note: This information was accurate when it was published, but can change without notice. Please be sure to confirm all rates and details directly with the companies in question before planning your trip.