The chance of a payphone being handy in the middle of a demonstration is pretty small. If you have to run a half mile to find a pay phone, then the strategy starts to break down.
However, if you want to try this, maybe The Payphone Project can help you locate the nearest phone. According to the listing for my hometown, it's likely a campground or cheap hotel.
Vertigo is often considered his best, but it's one of my least favorite among his best. Rear Window is my favorite movie, and I like The Man Who Knew Too Much, Lifeboat, and Stranger on a Train a lot, too. I've heard that someone is working on a remake of Strangers on a Train.