The Lexington Downtown Hilton is roughly a 15–20-minute walk from the venue. It has a free airport shuttle. 

• Hotel Rooms Near University of Kentucky - Hilton Lexington/Downtown

The Campbell House is very nice too. It doesn't have an airport shuttle. 

• Lexington Hotel | The Campbell House | Kentucky

Here's a general site about hotels in Lexington

• Hotels and Bed & Breakfasts in Lexington Kentucky - VisitLEX