No, it's not a Hummer with machine guns, it's not an Abrams tank, it's not even the Batmobile. It's a blimp.
Zombies, road warriors and tumult under the Earth's crust can't reach you when you're 7,000 feet in the air. Unlike the cars you see in those movies, if you give the blimp solar-powered engines to supplement the gas ones, you can stay up without refueling for a long, long time. The Goodyear blimp has space to carry passengers that can be used to store fuel, food and water. I would bet that you could develop a clever anchoring / winching system that would allow you to bring the beast down to land, particularly if you weren't worried about the property damage you might do if you snagged your anchor into a building as a mooring. Throw in a sniper rifle or two and perhaps some other weapons systems to clear away the undead when you cruised into town for supplies and you've got a pretty formidable apocalypse survival machine.