May is the obvious window — Pioneer Days Rodeo runs in the first week, the wildflowers are out on the prairie, and the weather is at its best. Summers are hot (regular 100°F days in July) but the heat is dry and the long evenings are usually pleasant. Spring storms can be violent; this is in the heart of Tornado Alley.
Winters are cold and windy with intermittent snow, and the panhandle's lack of trees means the wind hits hard. November and December are the quietest months for visitors. Avoid the worst of the late-summer heat in late July and August unless you have business that requires it.