I would advise extreme caution.
'There be demons' south and inland from Cabo Roig and if you venture to far you may well fall off the edge of the Earth.

However, if you are the adventurous sort, and you are prepared to encounter people that actually speak Spanish"¦"¦
Lorca,
Orihuela,
Cartagena,
Mar Menor (La Manga)
Mojacar (Costa Almeria)

"¦"¦ .to name but a few places worth a visit.

It is a very good idea to hire a car in the area as the local bus services are so poor and you get to see a lot more - try the town of San Miguel for some nice restaurants for a start! There is a car hire firm on the La Regia side of the N332 at Cago Roig roundabout, which I hjave not used, but have heard a reasonable.

However your best bet may be to hire a car from the airport as then you will save on a taxi / lift from the airport. Many car hire firms in the area do not refund any petrol in the tank and charge you for a full tank upon collection (a trick to get more money out of you in excess to the initial reasonable car-hire fee), however 'Car Jet' (their Spanish website is also in English) will refund any fuel in the tank on top of what I have found to be reasonable hire prices. Some other car hire firms also charge high deposits that are unreasonable so be careful who you book with.

Car Jet operate from both Alicante and Murcia airports and also have an office in Torrevieja (but I think their prices maybe more expensive from there).

One final word of advice is to remove any car hire stickers from the vehicle as soon as you leave the airport. Car hire stickers instantly highlight you as a tourist to those people that pull the well-know tricks for robberies in the area.