FlyZone is a testbed architecture to experiment with aerial drone applications. Unlike most existing drone testbeds that focus on low-level mechanical control, FlyZone offers a high-level API and features geared towards experimenting with application-level functionality. These include the emulation of environment influences, such as wind, and the automatic monitoring of developer-provided safety constraints, for example, to mimic obstacles. We conceive novel solutions to achieve this functionality, including a hardware/software architecture that maximizes decoupling from the main application and a custom visual localization technique expressly designed for testbed operation. We deploy two instances of FlyZone and study performance and effectiveness. We demonstrate that we realistically emulate the environment influence with a positioning error bound by the size of the smallest drone we test, that our localization technique provides a root mean square error of 9.2cm, and that detection of violations to safety constraints happens with a 50ms worst-case latency. We also report on how FlyZone supported developing three real-world drone applications, and discuss a user study demonstrating the benefits of FlyZone compared to drone simulators.