It depends a lot on what you’re after, since the season swings hugely. The core season runs from April to the beginning of October, with the party scene peaking hard from mid-July through August: biggest crowds, highest prices, hottest weather.
May, June and September give you the same clubs and warm sea with noticeably less chaos.
October is a different island: quieter roads, walkable heat, the last of the fig harvest still hanging in the air, and it’s genuinely one of the best months for hiking and exploring the sights and coves without the crowds.
If you want almond blossom across the countryside, that’s a late January to February thing instead, well outside the season, with most restaurants and clubs shut for winter. One thing to watch for if you’re travelling in autumn is Gota Fria: the intense, fast-moving storm systems that can bring flash flooding to the Balearics between September and November, so check the forecast before you go.