Late spring to early summer (May–June) is the best time: long days, the parks at their leafy best, café terraces in full operation, temperatures usually in the high teens to mid twenties. The big international jazz and theatre festivals run in early summer.
High summer (July–August) is hot — frequently into the 30s — and many of Zagreb's restaurants and shops close for two weeks while their owners join the rest of the country on the coast. The city empties out. If you are coming, you will find smaller crowds and easier hotel availability but less life.
Autumn (September–October) brings back the residents and adds the harvest: mushrooms, pumpkins, new wine. The trees in the Lower Town parks are at their most spectacular in mid-October.
Winter (December–February) is cold (regular sub-zero spells) and often grey, but the Christmas market — Advent in Zagreb — runs through December and has won the European Best Christmas Market title several times. It transforms the centre with stalls, mulled wine, and concerts.