Kyongju was a ruling seat of the part of the old empire, with some nice parks and historic sites. Having worked in Ulsan for several months, I have found my way to Kyongju many times. Among the highlights was Anapji (original name of Imhaejeon), a temple built around an artificial pond made as a bird sanctuary. Other highlights are Bulgoksa Temple, which is one of the largest, most famous temples in Korea; it is beautiful, but heavily visited. There was one Buddhist site, Sokkul Am, that I went to that was on a high mountain top.
On another particular visit I went back when it was cloudy and rather cool, but wasn’t too bad. As I went up, the clouds closed in with heavy fog, then rain, then snow. By the time I got there, the temp had fallen to -5C. The fog added a pretty cool mystique to the architecture and forest. So, as a testimonial, you should visit, rain or shine, winter or summer!
This is the university area of Ulsan. There will be many students and young professionals out. There are countless boutiques, restaurants, bars, PC-bongs, etc. You can find almost everything here either in the stores or being sold on the street vendors.
Went to Girimsa Temple, which was very nice. It wasn’t as large as Bulgoksa, but was cleaner, kept up and in a beautiful mountain valley. If the time of year is to your advantage, the mountains and temple have many cherry blossoms that bloom.