I would use 4" recessed low voltage lights. they are represented by the the darkened circles that I have drawn on the attached image.

also. I would use three sconces at shoulder height as indicated by the darkened rectangles. one between the sinks and one to the left of the first sink (closer to the entrance) and another one to the right of the sink by the tub.

is there a reason for the sinks to be so far apart?

I did a page on bathroom lighting ideas a little while ago which might be helpful. http://www.houseplanshelper.com/bathroom-lighting-ideas.html

dimmable is also a good idea - low light for baths and early morning or bright for shaving in the shower and applying makeup.

Thank you, the drawing is super helpful! I think that we will end up with the sinks closer together with some shelving on the side.

I did not mention line voltage or LED lights.

they could also be used. low voltage allows for smaller lights as does LED.

however, I find that low voltage and line voltage lighting work better on dimmers. that is, they appear much dimmer than LED lights.

I have not experimented with LED recessed cans. I have experimented with LED bulbs that replace MR16s in low voltage recessed cans and they work haphazardly with dimmers. they work just fine if no dimmer is involved.

you will need to check with your local building department about what requirements that they have.

they may require motion detectors to turn lights on and off. they definitely will want the line voltage and low voltage lights to be on dimmers.