I searched for off centered vanity in the bath section and there are many options..Here are some

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I think changing to a medicine cabinet or framed mirror is not going to work in this case. It will look crowded with the window. I'd keep the mirror as is.

for a kids bath, i really think its fine. for a mirror to fit over the sink it will either look crowded or be undersized.

A question, do you like the window being open to the space? You basically have two choices a narrow mirror to the right of the window keeping the offset sink or you can change and center it or leave it then float a mirror from the ceiling centered on the wall. This will cover the mirror but is very affective in balance out the space and adding some privacy, if you need it. You do not have to center the sink as long as the mirror is properly centered on the wall. Also note that this is an exterior wall so any medicine cabinet will not be recessed and will come out from the wall 4-5". This could become very bothersome as it will further accentuate the lack of balance on that wall. Best of luck!

Another option is to remove the window. You mentioned that you can't relocate it, however it could be closed off altogether.

If that is the only window in the room, I wouldn't remove it. I have a Jack&Jill bathroom that only has a small window in the tub/toilet room and I don't like it.

Do you need the window for light? If not, I would cover the glass with a pretty piece of art work (using the window frame as the art frame. I would put a rectangular mirror over the sink and under the window build a small shallow storage cabinet that will hold the tooth paste, brushes, etc. Naturally painted the color of the woodwork around the window/art. Put doors on it, naturally. Or if you do not want the window in the bathroom, take off the frame work and build a storage cabinet that covers the window..