(nb, I know this is a double post to two *different* sub-forums)
Just got back from Alcudia, we generally stay as Los Delfines apartments which are a 10 minute walk from the port as my father has a place there.
For the past 4 or 5 years we've always tried to fit in some sort of visit around the end of June. This is when Alcudia (and Pollensa to some extent) have the Sant Pere Fiestas. Not 100% sure what the Fiesta is for ... I think it's something to do with the Fishermen giving thanks.
Anyway, the port is MUCH more livelier than it usually is, with many events happening and a lot of small fairground rides for the kiddies. Much of this goes on very late into the night.
The culmination is a spectacular massive free fireworks display at about 12:30 at night. In my experience this has always landed on the last Saturday of the month of June but more information can be found at thealcudiaguide.com/alcudia-guide-fiestas.asp
I took some video on my iPhone (which really doesn't do it justice) http://youtu.be/aGb7yNwXabQ ; this year (which I hadn't noticed in previous years) they added a section where fireworks would be directed into the bay itself and explosions on carefully placed boats would happen (about 50 seconds into the video and again at 3:54). It's hard to say when the real finale of the display starts - maybe about 6:20 into that video. Bare in mind to, that I only took a few clips and cut them together; that's not the entire display which is about 20-25 mins long. The sound is incredible, and much of the display it assaults your senses, but the finale you can feel throughout your body as the booms shake you to your very core.
After the fireworks the party continues well into the daylight. Bars that you've never seen open near the port are rammed full of people as you are walking past in the early hours of the morning.
We've also been previous years where they've done fire running through the streets of the port. basically people running around with a lot of fire and fireworks on them and throwing fireworks on the ground. H&S nightmare. Not sure if they still do it; if they do then I've missed it.
Anyway, if you're wondering when is a good time to go, you wouldn't go wrong trying to get that festival in your plans somewhere - especially that last day.