Hi sugarmummy
A little bit of info regarding where to park in Murcia.
There is an underground car park in Murcia City. If you cross the river toward the Cathedral as you drive along with the Cathedral over to your right you should see it. It’s actually sited below the gardens and fountains. There is also a car park at Real Murcia FC old staduim next to the bullring in Murcia City.
There is a train timetable at http://horarios.renfe.es/hir/ingles.html you could always take the train from Balsicas to Murcia.