We consider the combined problem of frontier exploration in a complex indoor environment while seeking a radio source. To do this in an efficient manner, we incorporate radio signal strength (RSS) information into the exploration algorithm by locally sampling the RSS and estimating the 2-D RSS gradient. The algorithm exploits the local motion to collect RSS samples for gradient estimation and seeks to explore in a way that brings the robot to the signal source. This strategy avoids random or exhaustive exploration. An indoor experiment demonstrates the exploration algorithm that uses this information to dynamically prioritize candidate frontiers and traverse to a radio source. Simulations, including radio propagation modeling with a ray-tracing algorithm, enable study of control algorithm tradeoffs and statistical performance.