Its all relative, Central america is not as bad as its reputation, you just need to take precautions as you would in any big city in the world. Use common sense, keep valaubales hidden, dont show off wealth and don't take any unecessary risks. Whether you go alone or with a group poses the same risks really, though you may feel more safe with other people.
The government of Honduras is working hard to improve safety throughout the country for both citizens and tourists. Safety in most cities are comparable with other big cities around the world. It is advisable not to carry a lot of cash. Store any valuables in your hotel's safe when possible and keep a copy of your important document numbers (passport, visa, travelers checks, etc.) in a safe place.