we have an earlier thread on buses
http://www.holidaytruths.co.uk/forum/busses-rhodes-t159420.html
Have you thought about a couple of boats trips? You could just have a day sailing round the coast. We first visited Lindos on one of these. You can also do a day trip to Symi or even to Turkey ( Marmaris). I can't say if they are any good as I haven't done them. if you are not really ones for sitting on the beach all day you might want a day in Rhodes Town. Lots to see and do there. I loved walking around the medieval part. And of course there is shopping. I would absolutely recommend a day in Lindos. It is stunning. You can go up to the acropolis( very hot walk though) but you really have to take time to wonder around Lindos itself. It has narrow streets( no vehicles allowed) and loads of lovely little shops and tavernas .Some of the bars are one offs- very old and quaint. It is a great place for people watching. It also has the beach - not the best one you will find but good for a cool down.
There is a trip to the Valley of the Butterflies( hopefully I am on the right island here!). And of course you have your own resort, which I gather is really nice. I honestly can't remember it, apart from it having a big beach. Other folks will hopefully have up to date info for you.