Within Fun West you can stay overnight. If you want to use a tent, you will need to bring your own. There is plenty of space.
If you prefer to go outside the premises, the nearest place (4km) is Hotel Pueblo Acantilado.
Also check out this link of accommodation in El Campello (8km) or of course Alicante (20km); recently selected as the best city in Europe by the best combination of an airport, beaches, sun, going out!