There are small hospitals on Provo and on Grand Turk, and clinics on the smaller islands. Clinics generally operate 9am to 5pm Monday to Friday, and post a number for out-of-hours emergencies.
Provienciales and Grand Turk are the only places on TCI with larger medical facilities, although clinics are established in all settlements of any size. Visitors have to pay for medical are, and serious conditions will require relocation to Providenciales or Florida.
The water is safe to drink, although of variable quality depending on the island.
Regular travel and health insurance should be sufficient coverage for TCI. Consult your insurer if you're unsure.
There is no need to get anything beyond routine vaccinations when visiting TCI. For up-to-date and detailed information, see the Centers for Disease Prevention website (www.cdc.gov).