We investigate the problem of efficient data collection in wireless sensor networks where both the sensors and the sink move. We especially study the important, realistic case where the spatial distribution of sensors is non-uniform and their mobility is diverse and dynamic. The basic idea of our protocol is for the sink to benefit of the local information that sensors spread in the network as they move, in order to extract current local conditions and accordingly adjust its trajectory. Thus, sensory motion anyway present in the network serves as a low cost replacement of network information propagation. In particular, we investigate two variations of our method: a) the greedy motion of the sink towards the region of highest density each time and b) taking into account the aggregate density in wider network regions. An extensive comparative evaluation to relevant data collection methods (both randomized and optimized deterministic), demonstrates that our approach achieves significant performance gains, especially in non-uniform placements (but also in uniform ones). In fact, the greedy version of our approach is more suitable in networks where the concentration regions appear in a spatially balanced manner, while the aggregate scheme is more appropriate in networks where the concentration areas are geographically correlated. We also investigate the case of multiple sinks by suggesting appropriate distributed coordination methods.