Head north towards the river for the main sights of Murcia plus the city centre shopping area, which are on the other side. Don't miss the Cathedral, the Casino (you pay to go in however you can get an audio guide in English, which friends told us was very interesting), and the many plazas. Look out for the Ayuntamiento once you cross the bridge: the Cathedral is just behind it, plus there is a tourist office on the plaza where you can get a map and a city guide in English.
I am planning to do a write up of Murcia for my blog, but depending on when you go it may not be written in time!
Any more questions, I will try and answer them, though we are in the UK until Tuesday.
Sue