When and where was the first rodeo held ?

Aside from the work-related "roundups" of Spanish/Mexican vaqueros and American cowboys:

"The first formal rodeo contest probably was held in Cheyenne, Wyoming in 1872. Between 1890 and 1910, rodeo emerged as public entertainment through various Wild West Shows and performances at Fourth of July celebrations and cattlemen’s conventions.
Not until the first decades of the twentieth century did rodeo become recognized as a competitive sport. Annual stampedes, roundups and frontier day’s events attracted regional audiences and contestants through the West, often providing the only entertainment for miles. By the mid-1920's, with the help of early promoters, championship events at Boston Garden and New York City’s Madison Square Garden attracted nationwide focus."

Much more at: The History of Rodeo