Hi there, Manolo.
OK, more than anything, the best parties to attend depends on what kind of music you want to hear. Since you're going to Ibiza, I'm going to assume you're more literate in electronic dance music than most of our fellow Americans who still call everything "techno" or "electronica". The most interesting parties during that time period, in my humble but correct opinion, are:
June 21 - big choices here.Subliminal @ Pacha - New York's own Erick Morillo with Felix da Housecat as a guest. I'll admit to not being a huge Felix fan but Erick will play some straight up house for you. If you're more into techno, then Meganite @ Privelege is more up your ally, headlined by Mauro Picotto. My personal choice for that evening is La Troya @ Amnesia. It's a gay party that attracts a very mixed crowd (I'm straight) but has a really fun atmosphere. Expect house in one room with harder sounds in the other.
June 22 - If you like trance music then it's got to be Cream @ Amnesia but I personally would choose Renaissance @ Pacha with Hernan Cattaneo, Tiga and Desyn Masiello. It'll be an evening leaning towards progressive house.
June 23 - On Friday two top house DJs, Pete Tong and Steve Lawler, are co-hosting at Pacha which looks like good value for money. Alternatively, this forum's own Fronty will be among the DJs at a joint night of his How Clean Is Your House project (playing dirty bass house beats) and Pukka Up. That's at Es Paradis, which is not among the favorite clubs of the veterans but might be worth giving a shot.
I take it you're leaving the 24th so I'll leave it at that. Hope that helps!