14 days Itinerary - Seoul, Busan, Gyeongju and another spot?

Hi,

Im currently planning my 14 days trip to Korea next April.

While I've already visited Seoul a long time ago, I plan to visit the place again to meet up with friends for a week while staying in Korea another week by myself.

Up and until now I've planned that I'll stay:

• 5 or 6 nights in Seoul
• 4 nights in Busan
• 2 nights in Gyeongju.

Does any one have an idea where to spend the final couple of nights that I've got? I fear Seoroksan might be too much of an hassle to reach with public transport (Seoul > Seoroksan > Busan).

Or any Day Trip recommendations from the places mentioned?

From Seoul I'm planning on doing day trips to Suwon as well as Bukhansan, and skip the DMZ (been there before).

Appreciate the help!