I can recommend the Bonanca 2A apartment in Peurto Pollensa. Two of us stayed for a week at the beginning of August 2012 and it suited our needs perfectly. My husband used this as a base for cycling and I was able to enjoy the beach (about 2 minutes away) and pool.
The apartment is clean, a good size and in a good location at the quieter end of Pine Walk (just behind the Illa D'or Hotel). There is a small supermarket below which sells all the essentials and a good size Spar and bakery about 3 minutes walk away. The pool was a good size and was clean (although after a windy night there could be a fair few pine needles floating about). There are good toilet facilities at the pool and a nice bar/restaurant attached. My friends kids loved the pool and would join us here when not at the beach. The location is approx a 10-15 min stroll to the first of the main restaurants (excluding the Illa D'or), but walking along the sea front of an evening was never a chore.