Hi..!
We are staying here: Av de Elche, 3 03008 Alicante
But I wanted to drive around to other places - like Benidorm and Torrevieja.
Cool, so about 5 mins from the bus station. You can get a bus from Alicante to Benidorm return for just 8.25 (i think) and it takes around 30 mins and it takes you to the top of Benidorm, or 40 mins if you want the one that goes to a stop by the beach. Its pretty much the same time as driving. Just remember its not just the cos of the car rental and petrol.
For example if you take the coastal roads to places like Benidorm and Torrevieja then it will take a lot longer and cost you more in petrol, if you take the motorways then it will be a lot faster but it will cost you to use the road.
The buses and trams are really good, and they run all night (bus not tram). They are really safe to if you get the Alsa bus, and you can travel pretty much anywhere and everywhere.
There are 4 tram stations in Alicante too, they only go north, so places like San Juan, El Campello, Terra Mitica, Altea, Calpe, Denia. The tram is fairly slow though, but very cheap.
If you do go for a car then we normally go Europcar.
Also Spain is a nightmare for parking and that costs a lot too.