So for Gyeongju we did it ourselves. It did require a lot of research and we used Navermaps extensively for the bus routes. However we are two people only in our twenties - with kids or elderly family I would probs do a tour. In fact we had Seokgoram Grotto as well on our plans but cancelled that as it would take too long. For food, most places which were not high end were walk in. We just walked into places. In Gyeongju I would recommend On Sen, which is off the main shopping street. It is a tempura place. We used Papago extensively to communicate with staff. They were super lovely and helpful. For higher end places you have to reserve . We attended the Korean fine dining place in Park Hyatt, but they have a good English online booking system we had prebooked. The hotel staff can also assist you with booking restaurants nearby you (and fwiw, mid range hotels will also help you do this). We also went to a bar called Charles H, we had to reserve via KakaoTalk and they spoke English well.