There are plenty of car hire companies in the area, I can recommend a few if required.. It is easy to drive around the area/sites from Antalya down to Side and further down to Alanlya to include Perge/Aspendos etc.
Once you leave Belek/Kadriye you head upto the main D400 and turn left for Antalya or right heading towards Side. Very easy.Im there myself in August but not your hotel.

Close to your hotel is a place called Kadriey where there is a tour operators called lets go travel ,there you will be able to hire a car or book organised tours at a fraction of the cost you would pay from all the major operators .They will take you on people carriers where you are not traveling with a whole load of other tourists or if you want with the big buses ,your choice .There are plenty of great places to vist near you ,places of historic interest like the ancient city of Perge and Aspendos one of the oldest amphitheatres in the world where they still hold concerts at certain times of the year. The accustics are wonderfull .There are also places like Antallya ,Alanya ,Side within less than an hour drive.Antallya is loaded with really good shops, also the ancient marina with some of the oldest houses in the area and some great restaurants built on small winding streets surrounding it .There you will find one of the oldest Mosques in Turkey .Although the resort of belek is quite there are plenty of places to visit in the surrounding area .

Thanks so much for your replies - it all sounds great - just what we are looking for!
Thanks again,
Blue