Hotels frequently dress the windows of their rooms with a layer of heavy drapes over another layer of gauzy sheers. This seems like a practical solution for the home bedroom as well. It allows you to block most of your nighttime light and noise while leaving a portion of your window susceptible to morning light, and still achieving the privacy that a sheer curtain affords.
Curtains layered over fabric shades or blinds are another good option; lined fabric shades block out most light, but if you choose an unlined shade in a relatively lightweight linen, you'll get a good amount of light shining through in the morning. Slatted bamboo shades are a nice alternative, providing complete insulation at night but allowing a nice dappled light to shine through when the sun comes up.
Of course, so much depends on your own particular sleep and waking preferences. What's most important is to take stock of these before you choose your bedroom window treatments. Experiment, if necessary, by hanging sheets or blankets as temporary curtains to get a feel for how you sleep and wake up most comfortably. Give yourself several days of this trial period before you decide.
Feel free to weigh in below: How do you like your bedroom windows dressed?