In your specific situation I would mount a shaving mirror on the wall where the towel rack currently is. You know, one of the mirrors you can angle? I think this is one of the best solutions for your space. Hope this helped!

I wouldn't recommend that as I think it would obstruct the flow of the bathroom, being right in front of the door. But if the space allows go for it!

Is this a seldom-used powder room for guests or a bath that gets used every day?
I would not put a wall-mounted swivel in a powder room.

I assume you're prepared to replace flooring since you're replacing the entire vanity w/ a pedestal. Sinks are really nnot that big of a deal to move (toilets ARE). I think the best answer is to locate the new sink beside the toilet on the wall to the right. Then you can han a proper mirror above it.

Consider the amount of storage you will be losing & you may want to go with a small storage cabinet to the left side (under where the towel rack is now). You will need someplace to storage extra TP, etc.

This is mostly a guest bathroom although we do use it daily since it has the only toilet downstairs (all bedrooms/full bathrooms are upstairs). I will look into moving the sink by the toilet, that's a great idea! The bathroom has hardwood floors so I will have them matched and refinished.

I love pedestal sinks. Move the sink to the left wall where the towel bar is now. Maybe place a setee on the opposite wall.

It's always nice to have a place to set down a purse or lay out extra hand towels, soaps, cologne, aromatic oil, etc. Consider a free standing console centered under the window rather than a pedestal sink. Place a table mirror on one end along with a full length mirror on the back of the entry door. Or hang shutters on the window casing with mirror rather than wood inside the shutter frame. You can swing one toward you for checking make up etc. or swing both of them in for a view of your hair, front and back.