We are going back to Puerto Pollenca for the 3rd time this year. All of the apartments we've stayed in have been very nice, but none cheap.
Have you looked on Owners Direct website?

have you tried the hobby club apts

http://www.puertopollensa.com/rentals/

We are going to Villa Concha in October, never been before, but looks good in the broucher and on the internet site, and it was £500 for a week for the 2 of us.

Hi, we booked one via owners direct (came back couple of weeks ago), very nice though slightly close to the main road. The apartment itself though was beautiful and had a pool. The owners direct website is a wealth of info as is the puerto pollensa website

I know a nice one bed apartment if there is only 2 of you going?
1st floor apartment, shared pool, 1 minute beach, 15 minutes walk into port.