Galveston is a safe place, as long as you don’t wander out of the touristy areas. There is crime outside of these areas and occasionally crime may seep into them, so it is important that you are always aware. Most places are fine to walk around during the day, but at night you should opt for a taxi or to drive yourself. The Strand District is safe to stroll around in the evening, but please use common sense because just as in any city there could be someone waiting to target an unsuspecting tourist.