If you're visiting Split for cultural and sightseeing purposes, there's no better time than October and March. It's reasonably warm (for EU standards anyway), all the tourist crowds are gone, but the sights, shops and restaurants are very much open, as it's a living city of some 200.000 people, after all, which provides ample opportunity for people watching too. Not to mention that accommodation is way cheaper than in the high season.

(I've spent much of my life in Split, so excuse any bias )