I thoroughly recommend https://www.airbnb.co.uk/rooms/17298639
In Campanet (which has a couple of lovely restaurants and coffee shops). Great cycling in every direction including Batalla, Sa Calobra, Formentor, Soller and Fermenia. Pool very relaxing after a day in the saddle, a garage to keep the bikes in. 10 or 15 mins from great beaches of Alcudia and enough room to for two families. Cheap too ... we paid £10 per person per night! Sleeps 8 in four twins (one is a double).
I've already booked end of October!