Buses and trains regularly leave to Busan and other cities, the intercity and express bus terminal are very close to each other at the river in the southwest of the city. Take the #100 local bus, across the street from the express bus terminal, to get to Gampo.
KTX trains to get to cities northwest of Gyeongju require a transfer at Dongdaegu, however for short trips the Saemaeul will be cheaper, more comfortable and more convenient.
The travel time to Daegu by train or bus is almost the same but there are far more frequent buses and they're also cheaper. Express buses to Daegu and Busan run about every 10 minutes during the day, znd to either destination it's just under an hour.
a map of the local train destinations