Not sure what you mean by a "villa" but if you stick to the more populated area of Ubud and don't let your purse dangle off your shoulder, you'll be fine. (I did hear of a woman getting her purse snatched during a motorbike drive-by, but I'm not sure why anyone walking alone would let their purse dangle.) I think the best way to find housing in Ubud is to just show up at the bus/ shuttle stop. You'll immediately get offers for all kinds of rooms, usually in family/ tourist compounds (that all look like temples!), which makes for an interesting experience.