There's a castle up the coast a way from me, that's my hold up spot. Head up there first and lock it down. It has a working wall and gatehouse, fully fortify-able, on a hill with good views of the surrounding area. It's been left alone for a long time, so some work will be needed if I want to make the keep habitable, but the security of the curtain wall trumps that. It also has a well in the grounds, a river just outside it, and the sea not far away, as well as plenty of trees around it for firewood/building supplies.
First thing's first, I need supplies for the long haul. Head over to an out of town shopping area, call in at a new vehicle dealership on the way and pick up a nice big van. Fill the van with non-perishable food supplies (tinned goods, etc), hit the hardware store and stock up with essentials from there (solar panels and car batteries for electical items, torches, batteries, axes, hammers, nails, wood, etc). There's an outdoor goods store near that that sells fishing and hunting goods. Grab a few pairs of hiking boots, fishing tackle, bows and arrows (I already know how to shoot and arrows are reusable!), tents, camping stoves, anything that can come in useful. Take everything to the castle, lock it down and keep my eyes peeled. Any zombie shows its face I can wait until it goes away, or put an arrow through its head if it gets too close.