Energy optimization is a significant component of Wireless Sensor Network (WSN) design. In this paper we consider transmission energy optimization in WSNs where messages are collected by a mobile receiver (collector). The collector is responsible for gathering data messages by choosing the optimal path that minimizes the total transmit energy at the sensors subject to a maximum travel delay constraint. We show, both analytically and through simulation, that letting the mobile collector come closer to sensors with more data to transmit leads to significant reduction in energy consumption. Using this intuition, we propose an algorithm for choosing both the transmission radii and the mobile collector's path that achieves over 50% improvement in energy consumption compared to schemes that use a fixed communication radius for every sensor, and a 95% improvement as compared to the case of a stationary base station. We extend our results to the case of stochastic arrivals to the sensors and propose an Adaptive Algorithm that dynamically adjusts the transmission radii of the sensors based on the sensors' current queue sizes. We show that it can achieve 80% transmission energy improvement with respect to a non-adaptive scheme that uses fixed radii computed using the average arrival rates.