Dubrovnik receives visitors all year. Some stay in town for several nights, while many others (locals will say too many) arrive by cruise ship. You might consider scheduling your day trips for the hours when the cruise crowds arrive and fill up the old town. Fortunately, they disappear come afternoon and by sunset the city is yours again. The city is at its liveliest during the Summer Festival (mid-July to late-August), with everyone from international performers to backpackers scrambling to find a room in the Old Town. Some hotels offer Easter and New Year packages, so you can expect Dubrovnik to be surprisingly busy at these times, too.
The rest of the region is more easygoing. The July and August high season brings an influx of foreign visitors, mainly from Europe. Prices rise significantly during this period, as do temperatures; as compensation, the long summer evenings offer cultural performances and late-night drinking under the stars.
Low season runs from November through April, a period when many hotels and restaurants close completely. That said, through winter you may be lucky enough to find bargain-priced accommodation and blissful days of sunshine and deep blue sky, albeit with a bracing chill in the air. For most people the best time to visit is the shoulder season, May through June and September through October. You'll find no crowds, decent weather, and a chance to tune into the local way of life.