Day trip route
Nara is the easiest big day trip from Kyoto. The JR Nara line runs straight there in about 45 minutes, and the ride is free with a Japan Rail Pass, so most pass holders should ignore the private alternative.
Kintetsu limited express trains reach Kintetsu Nara station in about 35 minutes, and Kintetsu Nara sits closer to Nara Park than JR Nara. But Kintetsu is a private railway, so a Japan Rail Pass is not valid and you pay around 640 yen plus a limited express supplement.
The 10 minute time saving rarely justifies paying twice when your pass already covers JR.
Leave Kyoto by 09:00 and you can see Todai-ji, the park and Kasuga Taisha before the afternoon coach groups arrive. Many travellers pair Nara with Fushimi Inari, which sits on the same JR Nara line just five minutes from Kyoto station.
Quick answers to common questions.
Yes. The JR Nara line, including the fast Miyakoji rapid service, is fully covered. Kintetsu trains are not.
About 45 minutes on the JR rapid, or about 35 minutes on a Kintetsu limited express that the pass does not cover.
Kintetsu Nara is closer to Nara Park, but JR Nara is free with the pass and only about 20 minutes walk from the park.
Yes. Both sit on the JR Nara line, so you can stop at Inari on the way back to Kyoto.
Keep exploring Japan Rail Pass topics relevant to your trip.