I live in a small city, but there's a river at the end of my garden.
First I would secure the house as best I possibly could, and make some sort of basic floating device. There might be zombies in the water. Then I'd pack up with as many makeshift weapons as I could (I'm a uni student, so we don't really have lots of stuff lying around). Mostly kitchen-based. Knives, knives on the end of broomsticks, a pot or pan, maybe even a wok. And a grater, to get some badass kills in with.
During this preparation, I would phone as many friends as possible (I take it, by your admission that the radio words, I would have some coverage at least). Organize to meet outside the city somewhere. See if someone can get some walkie talkies.
Once the plan is in place, I'd set out on the river until I left the city, getting far enough out until I see less signs of infection, before heading cautiously inland to rendezvous with as many that made it as possible. I imagine several others would take the aqua route too, so I'll both meet with friends and battle any interlopers along the way.
I can taste victory already.