We loved our stay in Palma, it's the perfect location to explore the old town and there are loads of great cafes and shops nearby. We felt super secure here, there's a security gate at the front and the area is generally pretty quiet considering its central location. Pep was very helpful in recommending local places and he even loaned us a couple of bikes which were great for getting around. If you're into wine check out Cav. nearby on calle de la Gerreria for a selection of Mallorcan organic wines. For coffee I'd recommend Nanø Coffee Lab or the Rapha cafe. I've forgotten the name but there's a bakery around the corner where a 103-year-old grandma is baking empenadas daily - pretty amazing!
The apartment is north facing, so it doesn't get much light as it's a ground floor flat essentially. However the courtyard setting is wonderful and there's a fountain with fish that really adds a nice atmosphere to the place. The only thing I would change is the bed, which we both did find a little uncomfortable (too spongy/soft).
All in all we had a great time in Palma and would love to stay again.