You would possibly get more replies on the Costa Blanca forum as Torrevieja is south of Alicante on this part of coastline.Unless there is a Torrevieja on the Costa Brava that I dont know about.
You can catch a bus from the airport or drive yourself its a straight forward trip.just leave the airport and head for the A7 take the exit signposted Murcia.
I havnt been there but its home to many people who have bought one of the many homes that have been built there
Pipefitter

HI
I have lived in Torrevieja for just over 3 years and love it, Plenty of bars, restaurants, the water park opens end June. Beaches are great you have plenty to choose from. There is a shopping centre (Habaneras) which has about 64 shops.
To get to Torrevieja from Alicante ignore the Murcia sign head towards Alicante Sur then turn of at Santa Pola/Cartegena turn off, this takes you on to the N332 then it is a straight run. When you come out of Alicante airport you will see a blue sign which says Torrevieja IGNORE this as it will take twiceas long. Where abouts in Torrevieja are you staying? It is quite a big place

Hi Liggprob
Tried to PM you but unable to. Don't know about taxis i'm afraid think it may cost around 50+ euros from Alicante airport. If you ask the people you are renting from they may be able to help.

A taxi to Torrevieja will cost you about 45 Euro if you avoid the toll roads. Make sure you tell the driver to go down the N332 otherwise you will pay far more (I know people that have ended up paying 80 Euro through taxis going through toll roads from the airport).