The speaker wants to escape. Over and over, they imagine packing a bag and running, and the repeated "And run" works like a heartbeat or a pair of feet hitting the pavement. Each round of running has a reason behind it: first to get away from everything familiar, then to get away from an emptiness the speaker can't shake.
The poem builds a sense of momentum, and then it stops. When the speaker reaches "the place..." and tries to name a destination, the thought falls apart. "Wait I don't have anyone" is the turning point. Running only makes sense if there is somewhere, or someone, to run to, and the speaker realizes there isn't.
That realization gives the poem its mood: restless, lonely, and quietly sad. The speaker is already "alone," yet wants to get away from people and places they know. The ending suggests the real problem isn't a place at all, and that running can't fix the emptiness inside.