Apart from Cairns it's self most beaches to the north are sand. But as posted you have to go out a long way ti swim. Though having said that you would be looking for a north facing beach, rare! Buchans point just nth of Palm cove as mentioned but an un offical nude beach. Palm cove north all the beaches are sandy but if you are the inly one on a long stretch of beach in these waters well? Swim with a friend is a must. Trinty beach at the southern end is what you want or Taylor point and for this last name , please don't flame me. Even a lot of the locals din't know this one. Within a 15 minute drive or a public bus trip you can have a great sandy beach now a coral beach any where in the region that would be rare. From Buchana point and the Sapparo has just run out!
Having just read all the posts relating to this and having a few laughs especially about the big waves and rips at Cairns!!! Hello you are inside the Great Barrier Reef if it' above 50cm it's a cyclone.
You want Trinity beach southern most end and if your budget can afford it stay at Seachange. Now with the information in this and other posts
Have a shoot at using Google Earth. Oh and it' pure bliss here at the moment.