Korea has many tourist destinations, and Gyeongju has a vast number in a small area. I have listed the main tourist destinations as specified by the official tourist map of Gyeongju. As you can see, there are many locations to visit and many things to see. If you are in a certain area (i.e. Down town Gyeongju) you could quite easily see most of the major 18moa attractions if you wanted to, as they are often quite near to each other. All of the down town attractions are within easy walking distance of each other.
If you go to either down town Gyeongju or to Bomun Lake (where you will find the best international hotels) in spring - early to mid April - you can witness the blooming of Gyeongjus' cherry trees. They are absolutely beautiful and should definitely be on your itinerary if you want to visit Korea. Gyeongju is a tourist friendly town, and assistance in English is often available. Many American and British travellers make their way through Gyeongju, and foreigners are often seen cycling through the streets, and especially along side the river.
Once you are in town, you can get assistance from the tourist information center, in English, by dialing 1330 from a local phone. They have assisted me on occasion by providing me with local bus times and costs, among other things.