The obvious answer is the first Sunday in April, when the Tour of Flanders (Ronde van Vlaanderen) passes through and culminates nearby. The atmosphere around Oudenaarde on race day — with hundreds of thousands of cycling fans lining the climbs — is one of the great sporting spectacles in Europe. Book accommodation months in advance if you want to be there.
The rest of spring and early summer (April through June) is the best period for cycling the routes yourself: the days are long, the roads dry, and the countryside green. The Flemish Ardennes cycling infrastructure is extensive, with well-marked routes linking the famous climbs and passing through villages with cafes and estaminets.
Winters are grey and wet, as everywhere in Flanders, but the town hall and museums are open year-round and see fewer visitors in the off-season. The Kerselare pilgrimage is at its most active around the Assumption (15 August), and local fairs in summer bring some life to the Markt.