Nara outskirts priority

Hi there,
I will be leaving from Osaka on a late night flight so I would want to do something during daytime before returning home and I have been to Kyoto several times and Osaka as well. Nara have I seen twice the regular Nara park, the Todaiji, etc...

But I never been to the outskirts of Nara. As my time is not unlimited I would only get to see one or two of these probably, anyone of these you people on Japan guide would recommend to prioritate more than others?

Have you been to Uji?
http://www.japan-guide.com/e/e3975.html

Or have you seen Horyuji and the Heijo Palace?

Been to Uji yes, Thank you for asking. :)

But not Horyuji or the Heijo palace. I guess these felt to far away to see before so I skipped them...

There is a great Temple in "Hasadera', about 30 minutes train ride from Nara, Nice walk through township to park and Temple which is set up 'high' on mountain, about 15 minutes walk from the Hasadera Station, I enjoyed visiting there!...information about the train to Hasadera you can obtain from the 'Tourist Information Counter' at the JR Nara Station, the train ride to Hasadera was very 'picturesque'!....I will return there again, sorry I cannot give you more information.

I was gonna suggest Hasedera also.

Kifune/Kurama also comes to mind that many miss in Kyoto.

Either would be good for a 3/4 day trip.