Hell yeah it's safe for women to travel alone. Unless you're planning on walking around naked all the time, and even then your likely problems would be the risk of catching a chill and/or getting arrested.
Follow rules that you already do at home. Be aware of your surroundings, especially at night. Don't let your drinks leave your sight or, preferably, your hand. Don't believe a guy who drives up as you're walking home from school one day and says "I'm a friend of your mom's, get in the truck." Wait, never mind...
I've wandered into some really sketchy neighborhoods alone both in the US and abroad at night, and while I wouldn't advocate it, it's usually not going to end up with you being victim of a crime, either.
Your most likely annoyance will be guys pestering you for a date or hustling you for cash in full daylight in tourist-trap areas. Don't ask me why that is, it just is.