Is it safe to be around someone with a stomach virus?

If you're careful: If you are careful about washing your hands after touching things the sick person has touched and you avoid sharing drinking/eating utensils or having direct contact with oral/fecal secretions, you may escape. The sick person should also take precautions of sterilizing frequently handled surfaces (cellphones, faucet handles, door handles, tv remote, etc).

Usually yes: If you practice good hygiene (don't share food or drinks, wash hands frequently, etc.) the chances of contagion are low in most cases. If someone is immunocompromised or chronically ill, extra precautions or isolation should be observed. Some viruses which cause vomiting may be spread via the respiratory tract, but that is not as common.