Visited Korea this past month and wanted to concentrate mostly on places outside of Seoul as I had previously spent some time in the capital. Happened to land one day before the Lotus Lantern Festival which had a huge parade down the city centre so I had to stay for that.
First stop, we went to Jeju Island which is a popular holiday island for Koreans and others in the region. It had a bit of a Hawaii vibe and much more developed than I imagined but still had very scenic coastlines. I would recommend staying outside of the main towns to get that island feel. Great food, especially seafood and everywhere's pretty much set up for non-Korean speakers as well.
Next up was Busan, Korea's 2nd city where we hit up the main sites. It's a beautiful scenic city with a real different vibe from Seoul with workaday and laidback vibe. Would recommend the ever popular Blueline Train/Capsules which you'll have to book a month ahead of time these days.
Finally, our last stop in Gyeongju before returning to Seoul. Korea's historic capital was filled with historic and quasi-historic sites such as tombs, palaces, and temples. It was packed the weekend of Buddha's birthday but outside of the main drags it was quaint. That is, except the palace after sunset which was insanely crowded with everyone wanting to capture the place light up by spectacular lighting.