The third week of September — Walnut Valley Festival week — is the obvious time. Book accommodation (or campsite) well in advance and expect the town to be busy for those few days.
May to June and September to October are the most comfortable months for a normal visit, with green prairie, blooming wildflowers, and pleasant temperatures. Summers run hot and humid into the high thirties Celsius; winter brings cold winds off the plains and occasional ice storms. Tornado season runs April to June — keep an eye on the sky.