Worthington is worth visiting any time you happen to be in Columbus, but the most pleasant conditions are late spring and autumn. May and October offer mild temperatures, manageable crowds, and the best light for walking the historic district — spring blossom or autumn colour along the tree-lined streets adds something to the architecture.
Summer is hot and humid, as it is across central Ohio, but the outdoor spaces are usable and the Ohio Railway Museum operates its most frequent schedule on summer weekends. Winter is cold and occasionally icy, but the historic district is quiet and the buildings themselves are not going anywhere. If you want to time a visit around a specific event, the Worthington Farmers Market runs from May through October on Saturday mornings near the Village Green.