Klagenfurt has the warmest summers of any Austrian capital, partly because of the Wörthersee. From mid-June to early September you can swim in the lake, sit out till midnight, and rely on settled weather most days. The downside is that the whole city is full — every Austrian and a large slice of Germany seems to descend on the lake in July and August.
Spring and autumn are quieter and just as pretty. May is the time for the gardens at Maria Wörth and on the Kreuzbergl; October has the autumn colour on the surrounding mountains. Winters are cold and dry, with consistent snow on the surrounding hills from December to February — ski areas at Petzen and Gerlitzen are within an hour's drive. The Klagenfurter Sternsinger procession on Twelfth Night is worth seeing if you are there in early January.