OMG, yeah, unfortunately many creeps see a lone woman as a "crime of opportunity". I have been followed, too, on occasion.
Once, I did the same, Debra, I went into a store, "browsed" and chatted with someone in there.
This was on a sunny, beautiful Sunday afternoon on a busy downtown street. I passed this guy. I very briefly glanced at him just because he was standing there. He said, "What's a girl like you doing by herself here on a Sunday afternoon?" I kept walking. He started to follow. i walked into one store, he stood outside peering in. I walked out, passed by him, I went into another store, he did the same thing, stood watching me from outside. If I had been all alone, this could have turned into a confrontation. Had he continued I may have done something like this, waited until we were in front of a crowded cafe with a crowded outdoor patio.
I would have spun around to face him and angrily bellowed something like this, "What do you want? You have been following me for (X # of minutes) from place to place. So far I have been ignoring your attention-getting antics to let you know I am not interested. I don't know you, I don't want to know you. I do not want you following me and if you do not stop it right now I will have to call the police. Stop following me, now!!" That's probably putting it more politely than what I likely would say.
This was in my own city. However, this is what really happened ( although I have successfully scared a pursuer off by bellowing before). My hubby was in his favorite trinket shop just a few doors down, so when he was done, he saw me in one of the stores, came in. When the creep saw me talking to him and then him going towards the door, he took off.
Unfortunately, too, many creeps can sniff out tourists. They just have a way of knowing you're not from there. When I first moved here in my 20's, I felt very uncomfortable, too and some jerks said things to me to make me feel even more so. That was years before my training.
So, if there's people around, let them know by what you say to a creep that you don't know him (or they may think it's just a lover's spat), that you are feeling threatened enough to call police. Also, keep enough distance from him so that he cannot grab you, step to the side, step away, whatever you have to, to stay out of reach, and put your hands up in a defensive position. This is strong body language that communicates to anyone who sees you that you feel threatened and don't want this confrontation.
Depending on the sitch, during a similar situation, you could flag down a cab and have cabbie take you a far enough distance to elude the creep.