This paper describes the navigation strategy and path planning methods for autonomous road crossing by outdoor mobile robots in urban environments. Road-crossing is the part of outdoor robot navigation when a robot, while traveling along pedestrian sidewalks, approaches an intersection or a road crossing and needs to autonomously cross to reach the intended destination. In this work, the robot first autonomously travels along pedestrian sidewalks. For this, instead of using a pre-supplied navigational map, we endow the robot with the level of autonomy required such that it can spontaneously detect sidewalks and perceive a trajectory to navigate. While traveling along this trajectory, the robot performs real time detection of pedestrian push-button boxes. If a button box is detected, the robot deviates from the original trajectory and autonomously navigates to it. Next, using the detected button box as a landmark, the robot approaches the pedestrian crossing. It finally performs vision-based detection of the zebra crossings and generates the trajectory required to cross the road at a green signal. We demonstrate these methods are feasible by performing experiments with a custom built outdoor mobile robot using experimental conditions based on an actual pedestrian crossing in our university campus.