Stand behind steel fence (Not a flimsy chain link, PROPER FENCE GRRRRR), get something sharp, stab zombies all day long.
Walking Dead?
A prison would be a pretty great place if you really need to find semi-permanent shelter.
But in a Romero-style scenario, I would prefer to stay out in the open. I would escape and avoid congested urban environments as quickly as possible. I'd spend my days in large, open spaces like empty parking lots or grassy fields with lots of visibility just singling out zombies for extermination. I would favor melee weapons with long reach, that would allow me to dispatch zombies silently, at a safe distance, and limited only by my own endurance. So long as I stay mobile, there should be no reason to get overwhelmed by a horde. When I need to rest, I'd find small, sturdy buildings with two portals for entrance/exit. Before settling in, I would always arrange for some type of diversion that I can use to clear one exit and get back out in the open again. I imagine I could keep this up long enough to at least clear out a locality.
I would also head north and try to avoid warm weather, but also freezing temperatures (don't want to force myself into a shelter where I get trapped).
But this completely ignores the two biggest problems. First, my #1 priority would be to raid a pharmacy for insulin, which could go wrong in all sorts of ways. Everybody is going to be raiding stores for supplies, and it will be a highly crowded, hostile, and competitive environment. Second, I think the biggest problem in a real walking dead situation, realistically, would be a massive explosion of carrion population and disease, coupled with a breakdown of the societal infrastructure designed to deal with such things.
Edit: Oh and of course, I'd have my motorcycle gear, which makes me pretty much immune to human tooth/claw from head to toe. It's also not terrible heavy, being mostly just really thick, tough fabric meant to resist abrasion with some padding around joints. The only really cumbersome part to wear for long periods of time would be the helmet.