Kyoto and Nara are only half an hour apart by train, so you don't need to make separate hotel stops for each one.

Without a JR Pass, you can take the cheaper Kintetsu train to and from Nara. Its station (Kintetsu-Nara) is not near JR Nara, but Kintetsu Nara is actually a bit more convenient for seeing the sights.

Be aware, too, that you will need to pay for transportation within Kyoto and Tokyo. (Nara is completely walkable unless you go to one of the more outlying temples.)

Within Tokyo, you might want to opt for the Suica/N'EX combination ticket, which gives you a ride into central Tokyo on the Narita Express plus a pre-loaded reloadable debit card for train, subway, and bus transportation within the city.

The debit card for transportation within Kyoto is called the Miyako Card, but last time I was there, it was also possible to buy transit passes in 24-hour increments.