Hi Paws
I would certainly recommend car hire. It is possible to take taxi's but they are rather expensive (between €15 -20 each way). You could hire bikes at La Torre and it is only about a 20 minute cycle between Terrazas and either La Torre or Roldan, but if you don;t have a car, you really are going to be restricted.
For instance, even going shopping or picking up bits and pieces for your apartment would be problematic. The area aroud and about Terrazas is fantastic and well worth exploring and although there is a bus service from La Torre to both Murcia and the beaches, a car gives you much more freedom. Try doyouspain who provide the cheapest car hire quotes and you do not have to pay until arrival.
Good luck
Kim