Hi Sam,
No there are plenty of caves & limestone near Valencia
There are a few reasonable trips in this awesome book
GRANDES CUEVAS Y SIMAS DEL MEDITERRANEO. GUIA FOTOGRAFICA
http://tiendaverde.es/ficha.php?id=1350&lang=en
(i've only done one of them Els Sumidors & it was a nice day out)
Sima de la Llenca de Serrano (Tous - Valencia)
Sima del Campillo (Tous - Valencia)
Els Sumidors (Vallada- Valencia)
The most worthwhile cave in the area looks to be (worth the drive)
Los Chorros
http://viniloasesino.dyndns.org/~granchaman/croquis/chorros/chorros2/chorros2.pdf
and yes plenty more down towards Alicante see
http://gim-elx.iespana.es/gcv.htm
http://www.cuevasalicante.com/
regards
Beardy