What about:

 1. using 10:00 as default:
 2. only check for *weekend*
 3. you might replace `(str(day) in weekend)` by `(0 == day %6)` but it is harder to understand

Code:

    def alarm_clock(day, vacation):
        weekend = "06"
        if vacation and (str(day) in weekend):
            return "off"
        else:
            if not (str(day) in weekend):
                return "7:00"
        return "10:00"


The bit more cryptic version:

    def alarm_clock(day, vacation):
        if vacation and 0 == day % 6:
            return "off"
        else:
            if 0 != day % 6:
                return "7:00"
        return "10:00"