I live in SLC! I've never looked into rentals, but I did a bit of searching online.

Taylor's bike shop looks to do road bike rentals at their riverton location. This is the south end of the valley, so it may be too much of a drive depending on your time schedule. http://taylorsbikeshop.com/

Canyon sports says they have the largest road bike rental fleet on their website http://www.canyonsports.com/ but don't seem to list any information.

Hmmm...your best bet may be the bicycle transit center http://bicycletransitcenter.com/products-and-services They don't list the specific types of bikes available, but they are downtown and at a commuter hub. I would suspect they would have road bikes. This is where I would check first, above the other 2 I listed.