The following is a useful guide to parking at Alicante Airport and gives diagrams and instructions on short term parking. In addition to this, there is a drop off zone at Departures which is free for up to 15 minutes and intended as a quick way to drop off passengers. You take a ticket at the barrier and If you are under 15 minutes there is no charge, between 15-30 minutes will cost €1 but over 30 minutes you will be charged €18!
There are many options for long term parking at Alicante Airport but following are some options:
Low cost Parking
Marina Car Park
An alternative to parking at Valencia Airport is to take the train from Xeraco to Valencia which takes around an hour (free parking at Xeraco), then take the metro to the airport from the Xativa metro station which is situated right next to Valencia Nord station. The journey on the metro takes about 20 minutes.
Another option is to use the Alsa bus to Ondara. The bus goes direct from Valencia Airport on certain days, or you can get the metro from the Airport to Turia which is right next to the bus station. Go to the Alsa website and put your dates, etc into the form to get times, prices etc.