Also at the park is a full-on water park and a "culture expo" of some sort; I haven't checked out either.
Park hours can vary greatly depending on the season; in July they ranged from 9:50-18:15 to 8:50-20:45. Admission is 20,000 won ($20) and a free pass is 35,000 won ($35) for adults.
Google Maps has good bus information for Gyeongju (and most of Korea) so routing from Seoul can be done through its directions feature. It's also possible to take an intercity bus to Gyeongju and skip some of the steps above; ask at the visitor's center for whatever city you're in.
There is a visitor's center with minor English ability (enough to get directions and such) at the Gyeongju intercity bus terminal. The bus terminal clerks don't really speak English. As always in Korea, I recommend having your destination's name and address written in Korean characters to point at when asking directions or taking taxis.