Greece is a developed and stable democracy with a modern economy. A passport is required but no visa is needed for tourist or business stays of up to three months.
Medical facilities are adequate, and some in Athens and Thessaloniki are quite good.
U.S. medical insurance is not always valid outside the United States. Check with your own insurance company to confirm whether your policy applies overseas, including provision for medical evacuation. Ascertain whether payment will be made to the overseas hospital or doctor or whether you will be reimbursed later for expenses you incur. Some insurance policies also include coverage for psychiatric treatment and for disposition of remains in the event of death. The usual safety precautions practiced in any urban area ought to be practiced during a visit to Greece.