Spring (April–May) and autumn (late September–November) are the two civilised windows. Spring is also peak tornado season — the air is heavy and unsettled, and the National Weather Center is at full alert. If you want to see the place at its mythic best, this is when to come, but build flexibility into your plans for severe-weather days.
Summer is unpleasant: 35°C-plus afternoons, oppressive humidity, and grasshoppers in the parks. Football season — September through November — turns Norman into a different city on home Saturdays; book accommodation and a table well in advance. Winters are cold and dry with the occasional ice storm that can shut down the roads for a day or two.