Cover up, girlfriend! Cover your legs, arms (down to the elbow), shoulders, belly, and don't show cleavage. Basically, act like you're going to a Hindi temple, and you'll be fine. If you want to draw attention to yourself in a not good way, wear a tank top and short shorts. Kidding - please don't - it's offensive.
I wore wide-legged linen pants, light cotton kurtas (like a shirt dress), and always had a scarf with me.
On covering your head: There is no need as a tourist to cover your head - phew!