Deployment of cellular networks in urban areas requires addressing various challenges. For example, high-rise buildings with varying geometrical shapes and heights contribute to signal attenuation, reflection, diffraction, and scattering effects. This creates a high possibility of coverage holes (CHs) within the proximity of the buildings. Detecting these CHs is critical for network operators to ensure quality of service, as customers in such areas experience weak or no signal reception. To address this challenge, we propose an approach using an autonomous vehicle, such as an unmanned aerial vehicle (UAV), to detect CHs, for minimizing drive test efforts and reducing human labor. The UAV leverages reinforcement learning (RL) to find CHs using stored local building maps, its current location, and measured signal strengths. As the UAV moves, it dynamically updates its knowledge of the signal environment and its direction to a nearby CH while avoiding collisions with buildings. We created a wide range of testing scenarios using building maps from OpenStreetMap and signal strength data generated by NVIDIA Sionna raytracing simulations. The results demonstrate that the RL-based approach performs better than non-machine learning, geometry-based methods in detecting CHs in urban areas. Additionally, even with a limited number of UAV measurements, the method achieves performance close to theoretical upper bounds that assume complete knowledge of all signal strengths.