Stetson

A Stetson was a hat, typically found in the western United States.

When in Nevada in 1861, the Eleventh Doctor wore a stetson as an alternative to a fez. (NSA: The Good, the Bad and the Alien)

The Eleventh Doctor was given a stetson by Craig Owens. (DW: Closing Time) He wore it to Calisto B, Vegas 12, and the Seventh Transept before having the Teselecta impersonate him, still with the Stetson. The real version of the Doctor still wore a stetson while he was safe inside the Teselecta. (DW: The Wedding of River Song) In Utah, he met up with Amy and Rory and when Rory complimented him on the hat, he replied,"I wear a Stetson now. Stetsons are cool" before it was shot off his head by River Song. (DW: The Impossible Astronaut). Since it was actually the Tesselecta that River shot at, it is likely that the Doctor still owns the original.