Dynamic jumping with multi-legged robots poses a challenging problem in planning and control. Formulating the jump optimization to allow fast online execution is difficult; efficiently using this capability to generate long-horizon trajectories further complicates the problem. In this work, we present a novel hierarchical planning framework to address this problem. We first formulate a real-time tractable trajectory optimization for performing omnidirectional jumping. We then embed the results of this optimization into a low dimensional jump feasibility classifier. This classifier is leveraged by a high-level planner to produce paths that are both dynamically feasible and also robust to variability in hardware trajectory realizations. We deploy our framework on the Mini Cheetah Vision quadruped, demonstrating robot's ability to generate and execute reliable, goal-oriented paths that involve forward, lateral, and rotational jumps onto surfaces 1.35 times taller than robot's nominal hip height. The ability to plan through omnidirectional jumping greatly expands robot's mobility relative to planners that restrict jumping to the sagittal or frontal planes.