As Nara is quite close to Kyoto and does not take more than a day to visit it's not really necessary to book and hostel in Nara if you're staying in Kyoto.
It's a really nice place to visit and should not be missed if you're visiting Kyoto, at least for the deers ! Before going to Nara I did not believe the pictures with deers everywhere but I can assure you that it's really true and it's amazing ! They even bow to ask you some biscuits if you have some.
Nara was the capital of Japan before Kyoto. It was supposed to be a permanent capital, after a tradition of changing capital with each new emperor, but legends say that a monk was seducing the emperor's wife. As a result the emperor decided to let the religion administration in Nara and to move the capital in Kyoto.
Nara is therefore, after Kyoto, the second most important place culturally speaking. Eight Unesco World Heritage Sites are in the city.
One of the main asset of Nara is its size. Much smaller than Kyoto you can do most of it in a couple of days.
Nara was founded by empress Genmei under the name Heijo. It was the capital of Japan before Kyoto from 710 until 784. Nara, as well as Kyoto, was missed during World War II and holds a lot of[ Unesco World Heritage sites.