This paper studies how to select a path with the minimum cost in terms of expected end-to-end delay (EED) in a multi-radio wireless mesh network. Different from the previous efforts, the new EED metric takes the queuing delay into account, since the end-to-end delay consists of not only the transmission delay over the wireless links but also the queuing delay in the buffer. In addition to minimizing the end-to-end delay, the EED metric implies the concept of load balancing. We develop EED- based routing protocols for both single-channel and multi-channel wireless mesh networks. In particular for the multi-radio multichannel case, we develop a generic iterative approach to calculate a multi-radio achievable bandwidth (MRAB) for a path, taking the impacts of inter/intra-flow interference and space/channel diversity into account. The MRAB is then integrated with EED to form the metric of weighted end-to-end delay (WEED). As a byproduct of MRAB, a channel diversity coefficient can be defined to quantitatively represent the channel diversity along a given path. Both numerical analysis and simulation studies are presented to validate the performance of the routing protocol based on the EED/WEED metric, with comparison to some well- known routing metrics.