Stay in Seomyeon as it is central for hopping around. Also lots of nightlife and food for the evening. Also shopping.
Spend one day in Nampo-dong: Busan Tower, Fish Market, International Market, Culture Village. That is easily a whole day.
Day Two: Head out to Haeundae or Gwangali Beach if the weather is nice. Take a visit to Shinsegae Spa Land, a verrrry fancy Korean spa. Also world's largest. It is located at Centum City Complex inside Shinsegae Department Store.