IT IS AN EXTREMELY BAD IDEA UNLESS FULLY COVERED BY INSURANCE AND EVEN THEN MAY BE A VERY BAD IDEA IF HE IS NOT USED TO US CONDITIONS
You need to be absolutely certain that your "coverage for other drivers" does in fact cover him fully. There will be requirements re drivers licence that he must meet (not only will he need to have one but will probably need to have it with him) and if he has had accidents or convictions or certain medical or health conditions he may not be covered. You MUST NOT ASSUME he is covered. Specific checking with your insurance company is essential and having their agreement and terms in writing is "immensely wise". If you are 'scared' to do this because they MAY say no you will be even sorrier if they decline cover after an accident.
If a person is not covered by insurance for damage or injury that they cause then it can be extremely costly worst case and even in extremely minor accidenrts can cost thousands of dollars.
In addition, as owner of the car you may be responsible for the cost and/or legal consequences if he does not or cannot pay and may be legally liable for penalties quite regardless of money aspects. Your profile says you are in USA. I have no related expertise but expect that the potential consequences COULD be immense. At an absolute minimum he should be covered by relevant accident and liability insurance.
Generally insurance cover for tourists is an extra cost and he is liable to need cover that is specifically relevant.
The minimum cost he (and or you) could be liable for is complete replacement cost of an "up market" vehicle if he was in the wrong in an accident", and above that could be liable for personal damages which in the US can easily be hundreds of thousands of dollars and perhaps millions.