I like where you're going with this. I also like the contrast from the black face to the green back drop. However, the thought that came to my mind when I saw you're logos' was,'it's a hair salon logo.'
Would you be able to change the face and put some other image that relates to tanning? Also, if you can change the color from green to a more "warm" color?. Add a pupil to her eye, if it's going to stay open. Or if you drop her eyelashes so that they are only on the bottom part of the eye, then they will appear as if they're closed, and therefore they won't require a pupil.
One more thing, if you can choose another color for the face, rather than black or green.
Thanks,
Alicia