In Nara, there is a large area where various temples and shrines are located, deers would be roaming about while you take a stroll among the temples. Feel free to touch the deers and take photos with them.
During summer (is generally around August), Candle Festival would be hold in Nara. The whole area will be lit with candles from approximately 5pm to 10pm, it looks magnificent at night.
It is strongly recommended to go during Candle Festival, unless if you’re an absolute deer-lover, then anytime will work for you.