In your diagram it looks like the sink is offset in the vanity, but in the example you show it doesn't. It doesn't really matter. In either case I'd do a wall to wall mirror in the alcove. I'd center lights as well. You brush your teeth over the sink, but maybe put on makeup over the counter portion.

Thanks @Linelle! Great point about doing makeup/hair over the counter vice sink. You've made me feel a lot better about centering the lighting (my biggest concern). Husband--who won't stop complaining about me "changing things"-- will be happy too!

Also, doing hair (brushes, product, dryers, irons). The blank area is where the beauty stuff happens. :)