It's a little far from Nishiijin, but Kenninji Temple is just down Hanamikoji Street in Gion. Even though it's a road, tourists ignore it and it's always difficult to walk or cycle through, but recently the police have been controlling it and it's now easy even for a car to drive through.
As the cherry blossoms were late this year, I have expected for the peonies to bloom also late, but they seem to have bloomed as usual... I missed this year the best timing, but some are still in full bloom!