Hotel Portixol - by the old harbour. I've stayed here 4 times and loved it. It's a small, personal, very relaxed boutique hotel, very Scandanivian in design, and the service is superb. It has a small pool with wonderful recliners, and is THE perfect place for a weekend getaway.
The food happens to be superb too, and the Portixol burger and strawberry shake, mmmmm.
It has changed over the years, it did use to be more informal and relaxed, but has been discovered by the Louis Vuitton beach bag brigade recently ;-) A bit too obvious if you get my drift.
Saying that, there would be no other place in Palma I would rather stay at.