You have asked one of the most loaded blanket questions in the construction field.....costs can run the gamut from $80 per square foot to $200 and up....the sky's the limit.
You could be assembling a pre-fab acting as your own GC and doing some of the finish work yourself to a top of the line custom log home with mahogany cabinets, granite counters, soapstone sinks, etc.....
$110 to $150 is a good range for the average home fully contracted out, but as you are probably aware Driggs has become an upscale haven for Jackson Hole refugees and is becoming pricey.....builders tend to se $$$ signs in their eyes when they hear this is where you want to build.
A way to get good value for your money is to buy a discontinued model log home, or one where someone put a deposit and never paid for the final order and the company discounts it, etc.
Down the road in Menan there is a builder named Randy South who builds incredibly strong, near disaster proof and super efficient homes (you can heat them with a warm personality) called Monolithic Domes.....they are about as far from a conventional home or log home as you can get but the benefits are many...
Here's a link to their site if you would like to investigate.....
Monolithic Dome Institute