Bingo! Thank you.
http://georgia.usembassy.gov/medical-information.html has turned up some good options.
Originally Posted by
MSPeconomist
If there's a USA consulate there, try to find out what medical facilities they would suggest or use for their own staff. Do any American companies have lots of expat staff there? If so, check where they would send their people. AmEx might also be able to make suggestions.
Does the teacher have health insurance for Russia? They might suggest or require certain hospitals.