I am looking for the name for that part of a public toilet where the mirrors are and you can powder your nose.
Apparently, it can be called a "womens lounge" if it's actually an anteroom with chairs and mirrors and perhaps a sink, but separate from the rest of the bathroom. It's where the co-toileters (?) wait.
When I have seen a women's lounge, it is usually a larger room outside a toilet/restroom with vanities and some seating for fixing makeup, waiting for the restroom to be available, etc. From the hallway you go into the lounge, then from the lounge into the restroom. Also, sometimes men are not strictly forbidden from entering the lounge as they are from the restroom.
In a public bathroom, you have stalls, urinals (if it's a men's bathroom), and sinks. Some "family" bathrooms will have a baby-changing area (just a pull-down table against one wall).
You say are you are looking for:
that part of a public toilet where the mirrors are and you can powder your nose.
If you are standing at that location, you are "standing in front of the sink."
Short of uncommon and fancy bathrooms, that might have a separate dressing room or vanity area, that's all public bathrooms are: a single room, with a few amenities in different locations.
If you're waiting in line for a bathroom, you are waiting outside the bathroom.
In a comment, you say:
Well, I'm trying to relate that something happened to a lady in the area I'm asking about while her friend was in the cubicle doing business. So in relation to each other, I need to situate each of them.
To describe this, you could say:
Both she and her friend were in the bathroom. Her friend was in a stall, and she was standing in front of the sink.