While there are several well-protected harbors, no anchoring is allowed as the entire archipelago is a nature reserve. However, in the main harbor there is something of a rarity in the Balearics: a mooring field. There are about 50 overnight moorings for vessels of differing sizes, and you must reserve them in advance. Be aware that reservations cannot be made until 20 days before your desired date, and in peak season they go very quickly. You can reserve a spot for 2 days during peak season, or for a whole week when it's less busy.
To reserve a mooring, follow this link. You will need the full registration/owner information for the boat, so if you are chartering make sure you ask for this before you try to place a reservation. I didn't* and it forced me to reserve a spot a day later than I had hoped, which cost us a whole afternoon there. Reservations are from 6PM local time on the day of your reservation until 5PM the following day. Unless you get stuck on one of the large-ship red moorings at the mouth of the harbor like we did (they were the last ones available), the moorings are in a quite protected part of the harbor. Even our more exposed position was relatively calm while we were there. There are also day-only moorings in the same harbor, and more on the other side of the island, but I am not familiar with how those are reserved.
So, with the "how" out of the way, let me get into the "why". Cabrera is absolutely beautiful. There is a small pier with limited facilities in the main harbor; the single best dinghy dock we saw all week, restrooms, and a small cantina that serves a variety of delicious tapas. (Note that, unlike many other restaurants on Mallorca, the cantina on Cabrera closes a bit on the early side at 9:30 PM local time.) There is a strict "no trash" policy, so don't expect to be able to bring any rubbish or recycling ashore. From the pier, you can find a series of hiking trails that lead to, among other places, a small medieval castle overlooking the harbor that is partially open to the public. The castle is definitely worth checking out even if you're not a history buff because the views of both the harbor and the Mediterranean are spectacular. There are also a few areas in the south of the harbor where you can dinghy ashore to beaches and some good areas for snorkeling, but we didn't get to any of them.
But the crown jewel of Cabrera has to be the stars. There is virtually no light pollution there, and with the high cliffs surrounding the harbor you get what Sara calls a "snowglobe" effect where the stars all feel close enough to just reach out and touch. On a clear night like we had, words don't really do the view justice. I'd love to go back an just spend a few hours ashore taking pictures of the stars.
One piece of advice: if you're moored near one of the cliffs in the harbor like we were, keep your anchor light on even though it's not required in a mooring field. Imagine motoring in your dinghy towards a massive wall of blackness, several times taller than your sailboat, that fills your entire field of view and trying to find said sailboat without any lights on it. Even with the anchor light on it was a tad disconcerting, but without a light on it would have been downright unpleasant.
We only got to stay for about 18 hours due to scheduling pressure, which is not nearly enough time to explore, but even in that short time we fell in love with the place. If you ever find yourself planning a trip to Mallorca's southeastern shore, I highly recommend at least a whole day stopover at Cabrera.
*The main base of the charter company did though, and they provided it quickly once I asked. It was the 6-hour time difference that really slowed us down though.