The site looks pretty nice.
I have no experience in web design, so no real technical input from my side, but I noticed it is inconsistent with the time representation.
You use the 12-hour AM/PM representation in the "I have to wake up at..." picker and in your text below that.
But the actual calculated bed time uses the (imo better) 24-hour format. This could lead to confusion, but at least is somewhat inconsistent.