I'd find whatever survivors I could, and somehow find my way to a small island somewhere. Maybe even Hawaii. With some luck, we'd hopefully be able to take out the zombie population there, and assume that the zombies in the mainland wouldn't be smart enough to make their way across the waters.
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Considering zombies have no need for air, water wouldn't be a very effective barrier against them. It may take them a while to get to the island, but they could shamble around underneath the water indefinitely. Plus, miss a few zombies already on the island and you're trapped in a confined area with a resurging outbreak.
I'd be more worried about the panicked mobs of people than the slow-moving undead, so I'd spend the first few days holed up in my apartment with all entrances barricaded. As long as I'm careful not to make any noise there wouldn't be much need to worry. Once the initial outbreak died down a bit I'd set out to scavenge weapons and supplies from wherever I can find them. Maybe try to join up with a few other survivors, but stay moving and away from any cities as much as possible.
Of course, that's all assuming these are the traditional shambling, dim-witted zombie hordes. We're all pretty much screwed if they can run.
Jam it back in, in the dark.