Houston is widely considered to be one of the safer big cities in America, this isn’t entirely correct.
Houston’s violent crime rate is 150 percent higher than the Texas average, which makes it a worryingly 170 percent higher than the rest of the US. However, this high level of crime is typically isolated to the ‘bad’ parts of Houston, with the more central and tourism focussed parts remaining areas to watch out for pickpockets and other more expected hazards. Areas to avoid include Sunnyside, “the Track,” and the dangerous neighbourhood that centres around the intersection of Dowling and McGowen Streets. Feel free to explore the city but plan your excursions first and maybe ask a local to advise on anywhere in particular you should keep clear of.
Treating most of Houston with the same caution you would use when in any other larger American city should see you fine throughout your trip.