An electronic device such as a head mounted device may have an inner display that displays an image for a user through lenses. Head-mounted support structures may be used to support the display and lenses. One or more external displays may be publicly viewable while the head-mounted device is being worn. The head-mounted support structures may have a front face on which an external display is mounted. One or more finger sensors that are configured to detect touch input, force input, and/or other input from an external object such as a user's finger may be included in the head-mounted device. A finger sensor may have an elongated shape that runs along a peripheral edge of an external display on the front face. Finger sensors may also be located on other portions of the support structures.