Interactive maps are now ubiquitous in our daily lives. Whether in the car or at the mall, maps help us find our destinations and discover more about our surroundings. Yet, interacting with maps is not straightforward and depends on the device the map is used on. As drones become more widespread, how will we interact with drone-based maps and navigation devices? In this paper, we propose FlyMap as a novel user experience for interactive maps projected from a drone. We iteratively designed three interaction techniques for FlyMap's usage scenarios. In a comprehensive indoor study (N = 16), we show the strengths and weaknesses of the techniques on users' cognition, task load and satisfaction. We then pilot tested FlyMap outdoors in real world conditions with four groups of participants. We show that its interactivity is exciting to users, opening the space for more direct interactions with drones.