Two week stopover in South Korea

I've got two weeks to kill in South Korea between month-long stays in Vietnam and Japan. I've been to Seoul, but it was a while ago and I'd like to see more of it. But, I'd also like to see Busan and Gyeongju.

I was thinking I'd land in Seoul, do 6 nights Seoul, 4 nights Gyeongju, 4 nights Busan and fly out of Busan. I know Gyeongju is small, but I tend to spend a lot of time just wandering/taking photos/relaxing in cafes, etc... and I really like history and architecture. So, I think 3 nights is too few for my travel style.

But, is only 4 nights in Busan too rushed for a first time visit? It's less time than I usually spend in a new city.... I could shave a day or two off Seoul, if Busan is worth adding extra time. I just know there's a lot of Seoul I haven't seen yet.

Thanks!