MowMow goes to Petco with me, either in his stroller or in the cart.
I keep his harness on him so he can't make a break for it. I don't THINK he'd ever go far from me, but I've never felt safe taking that chance with him.
Neelix has gone with me to Wilco a few times since I got him. He wears a little harness and sits on my shoulders (and in the cart).