I found an
excellent website with information about restoration projects at popular Japanese tourist spots, including the following World Heritage Sites:
Ancient Kyoto: Kiyomizudera Temple has restoration projects under way that are expected to be completed
in 2019. Currently, the Okunoin Hall, Amida Hall, and Shaka Hall
are being renovated.
Ancient Nara: The East Pagoda at Yakushiji Temple is currently being renovated and is covered by scaffolding; the restoration should be completed
in 2019.
Nikko: The main hall at Rinnoji remains enclosed by scaffolding, but remains open through its restoration, which is expected to be complete
in March 2019. Also, the prominent Yomeimon Gate at the Toshugo Shrine is also undergoing restoration and covered by scaffolding; this restoration is also expected to be complete
in March 2019.
I'm not including the Peace Memorial Museum renovations in Hiroshima since the Genbaku Dome is still accessible.