In a localized routing algorithm, node A currently holding the message forwards it based on the location of itself, its neighboring nodes and destination. We propose to use depth first search (DFS) method for routing decisions. Each node A, upon receiving the message for the first time, sorts all its neighbors according to a criterion, such as their distance to destination, and uses that order in DFS algorithm. It is the first localized algorithm that guarantees delivery for (connected) wireless networks modeled by arbitrary graphs, including inaccurate location information. We then propose the first localized QoS routing algorithm for wireless networks. It performs DFS routing algorithm after edges with insufficient bandwidth or insufficient connection time are deleted from the graph, and attempts to minimize hop count. This is also the first paper to apply GPS in QoS routing decisions, and to consider the connection time (estimated lifetime of a link) as a QoS criterion. The average length of measured QoS path in our experiments, obtained by DFS method, was between 1 and 1.34 times longer than the length of QoS path obtained by shortest path algorithm. The overhead is considerably reduced by applying the concept of internal nodes.