This page covers all details about car hire and driving in the Costa Blanca.
You will need to hire a car, the crags are abundant but widely spaced. Fortunately car hire is not overly expensive. Typically you can expect to pay £100 for a weeks hire of a Vauxhall Corsa sized car. This does include a tank of petrol when you pick up the vehicle and you bring it back empty. This saves the complication of having to find a petrol station the minute you turn up in Spain but it does always leave you with an interesting dilemma on that last journey. Just how far can you stretch those last drops?
There are all the usual companies; Hertz and EuropCar but these tend to be more expensive. Your better bet is the local companies. These have little vans parked in the car park at Alicante airport. They use these vans as their offices. You can hire a car when you get there but it is taking something of a risk that they have one available, what's better is to book it from home.
I have used both Victoria and Javea Cars before now and found the vehicles fine. Javea cars are based in Javea (surprise surprise) but all paper work can be sorted at the airport leaving no reason to visit the head office. They also accept MasterCard at the van.
'Used Premier - very simple procedure and very reasonably priced (they act as agent for the local firms), but you do get stung for the cost of that first tank of petrol. You don't pay over the odds for this, but it may be worth mentioning.'
Thanks to Ian Silvester for this comment.
If you don't fancy one of the van based companies you could always try one of the Spanish national companies. They have little offices downstairs from the arrivals hall.
Car Theft Warning
One word of warning, as stressed by Chris Craggs, car thieves have cottoned on to the easy pickings that climbers' cars represent. This in an international problem not just one at home, so don't leave things in the car and do remove the parcel shelf so that they can see it is empty.
Tips for Driving in Spain
Do, whenever possible, use the toll motorway, the AP-7, rather than the coastal road, the N332. The latter leads through all the coastal towns and is an absolute nightmare. Don't waste your holiday in traffic jams.
The motorway tolls have recently been reduced as the government has removed the Spanish equivalent of VAT from the cost. This is to encourage people to use the motorway however most of the Spanish still struggle up the coast road leaving the motorway wonderfully clear for us tourists.