You can buy plushie goats, mugs with goats on them and postcards with goats on them. Clearly, goats are a tourist attraction, but why?
Well, apparently there are two mechanical goats on the town hall clock tower, which butt their heads together at noon. There's a folk tale as to why they're there, something to do with the town hall's cook going to look at the clock tower instead of watching a leg of venison roast, then when the venison fell into the fire his assistant kidnapped two goats to use instead; these goats escaped and climbed onto the cornice, where they started butting their heads together. The event was commemorated by having mechanical goats butt heads on the clock tower.
It doesn't sound convincing to me, but Poznan seems set on having goats as its tourist-attraction mascot, so that's why they're everywhere.
I only learned the butting-goats story when I looked up why Poznan is obsessed with goats. I therefore wasn't aware of the mechanism on the town hall's clock tower, so didn't strive to see it in action.
I guess knowing where the town hall was would have helped, too.