If you are public property, you only need city permission. If you are in any of these stores you need their permission, but if they are only shown as you are on public property as your photo shows, you do not need their permission.
If this is just one shot of a woman walking down the street, I think I'd opt for guerilla style. If you have a boom or lights, I'd get the permit, but if it's just a camera and one shot, I'd probably steal the shot.
The best bit of advice I have received on this issue was, "The first time you get caught filmming something you're not supposed to, chances are you won't go to jail." I have done this a few times, and I haven't ben to jail for it yet. I say go for it.