Great discussion here!
Turns out the sun was up by 5:30 in the morning, and there weren't a lot of people around at that time, so I did just sneak out every morning. Surprisingly, the Strip is a fun place to run in the mornings, and there are quite a few runners even early in the day.
I like the flip-flop idea best. To me, VFFs are just as odd as bare feet, and I don't want to spend my money on them. OTOH, I do have a pair of Xero sandals, which are quite easy to carry while running, and which I sometimes carry if I'm worried about glass or thorns.
FWIW, I am in the swimsuit-with-pockets and Hanes Cool-Dri T-shirt category. I don't need to spend a lot of money to look like any particular kind of runner. They closed off the sidewalk in a few places due to construction, so at one point I found myself running barefoot through a casino. Nobody seemed all that bothered.