@Joseph V. the short answer is: yes, there are tons of places across the US where you can find a 3 BR / 3 BA house in a safe neighborhood. Is this for you to live in, or as a rental? Can you narrow a little bit?
Phoenix is one such place. 350k doesn't have the same pull it did a year or two ago, but you can still find a newer (2000 and up) home in a good neighborhood for 350k.