Problem with slow zombies is that they tend to be in mass hordes. Note that this isn’t because they’re herd creatures, but because of other, more basic, non social factors, that potentially make things worse.
The average slow zombie is very dumb, and just moves in the direction of sense stimuli (usually sound but could be sight too) in case it is food (since to a zombie anything moving is probably food). If you get multiple zombies hearing the same thing, they head off towards that, eventually meeting up. After they meet up, they are close by for when they hear the next thing, then happen to be traveling together and continually pick up more zombies. In some series, like the Walking Dead, they have these hoards can be over a mile in diameter, just wandering around with a common direction, mowing down everything in their path. Yeah, you can out run an individual zombie, but if you are hit by a horde you’ll have issues simply because of the size.
Problem with gun shops, shopping malls (or stores in general), marinas/harbors, airports etc. is that you think that “Yeah, I’ll just go to the gun shop to get, weapons, to store to get food and then to airport.” But that’s actually what everyone else is also thinking. So you’d very likely find a huge crowd of people fighting over the things you are trying to get. And the problem with huge crowds is, that they tend to spread diseases.
But yeah, if you could get a boat and a fishing rod/a net, you’d be pretty much covered. Just sail around the coast and have the longest holiday ever.
And the same thing with a chopper. If you get one and can fly it, then straight to a small island it is.