Nara has more UNESCO world heritage sites than any other prefecture. Todai-ji is a must-see. The temple is the largest wooden structure in the world and houses the largest Buddha in Japan. Also the deer roaming the streets make for great (/frightening) memories.
Don't miss seasonal events like the Shuni-e Buddhist torch ceremony, which has taken place every year since 752. Or watch the mountains catch fire at the Mt. Wakakusa Fire Festival.
No matter what you do in Nara, you'll no doubt be captivated by the experience.