Besides the root tips, where else in plants would you expect mitosis to take place?

There is a special type of tissue that mitosis occurs called meristematic tissue. The root tip contains apical meristem as you have mentioned. The stems contain apical meristem located in the terminal and axillary buds. This allows them to grow in length. The woody dicot stems contain a ring of meristematic tissue called the vascular cambium. This allows the plant to grow in thickness. Also the root contains an area of meristematic tissue called the pericycle. This is responsible for secondary root growth.