The James F. Martin Inn is located in the same building as the Madren Center and offers incredible convenience at a reasonable rate. Another option is the Abernathy, which is right next to Clemson University itself. It calls itself Clemson's premier boutique hotel.
The best airport is Greenville-Spartanburg (GSP). The Atlanta or Charlotte airports are an alternative option, but those are each a 2-hour drive from Clemson. Renting a car is likely your best option for transportation from the airport, but Uber and Lyft are options as well!