Sion is one of the driest and sunniest places in Switzerland year-round, which makes it a viable destination in any season. That said, timing matters:
Spring (April–May) brings the vineyards to life and is a good time for walking the hillside trails before the summer heat sets in.
Summer (June–August) is the best time for the hilltop sites — the ascents to Valère and Tourbillon are warm but manageable, and the old town is lively. This is also when the Valère organ concerts take place; check the schedule in advance and book early.
Autumn (September–October) is the wine harvest season and arguably the most interesting time to visit if you care about the vineyards. The hills above the city are busy with pickers, and the wine bars are at their most animated.
Winter (November–March) is quiet in the city itself, but Sion is a practical base for skiing at Crans-Montana (about 30 km by road) and Verbier (about 45 km). Snow in the city is common but not deep.