Zhizihu is a fertile valley below the Xiaoyoukeng volcano. In spring it is full of flowers and it is very famous to go to collect calla lilies. You can take a walk along some walkways between the flower fields, but the flowers are privately owned, so you will have to go into one of the many shops or cafes so they let you take pictures and even take some home with you... The price is usually 100 NTD per person and you can take about 6 flowers.
If you want to make a quiet coffee with the best views of the volcano, we recommend that you go to Cafe Hope (in the northwest area, you have it geolocated in the app). But if you go with children, perhaps it is better to enter the place next door, right at the foot of the observation platforms (it is worth going up to see the views). There is a lot of funny things for children there (like a pool with balls, some rabbit figures... they love it) and they can also put you in a waterproof suit so that you can enter the very field of calla lilies to collect the best ones (they also have children's size). The price is the same: 100 NTD for 6 flowers.
To get there, if you go by car or motorcycle, it is best to park in the area on the right. Here you will see that there are some walkways that take you north. If you go by public transport, take bus 108 to the YouYuan stop, and from here walk downhill for about 10 minutes. You can also continue a little longer by bus to the Zhuza Police Substation stop and there take bus 131 to Dinghu Entrance, but beware that this bus only operates in flower season (from the end of February to the middle of June more or less).