If you want to go to the beach but, when all's said and done, you get bored of just lying on the beach getting tanned, I recommend going to San Pedro del Pinatar. 50 minutes from Murcia (take the no. 70 latbus), San Pedro del Pinatar has a lot to offer: the beach, of course; the harbour; cheap bars and restaurants; a walk along the salt mines; mud baths; an incredible view of La Manga; nearby untouched beaches, flamingos to look at.
It couldn't be easier to get there: just take the number 70 latbus (the name of the company). They also leave every two hours on a Sunday too. You can get off at the last stop in San Pedro, next to the harbour. After that, you can go left and then along the beach until you reach the end of the Mar Menor.
There, you can walk along the dock which runs alongside La Manga, they almost touch as the passage in between La Manga and San Pedro del Pinatar is very narrow. Walking to the end and back takes about an hour and a half if you walk slowly.
You can also go for a dip near where the dock is: the water is warmer than the sea. People don't go there just for a little swim, but to cover themselves in mud that they leave to dry in the sun. The older people come here and chat in the water. They say it's good for the joints. But be careful of the smell... it smells a bit like rotten fish, haha!
If you want to go to the more untouched beaches, you've got to keep following the dock and go left at the first mill. There's a long and straight main road, then a roundabout, go left when you get there. If I remember rightly, it's all signposted. Then just keep going and you'll see some grassy paths which lead to the left and where you'll find the beaches. There might be a few nudists. :P
Enjoy the walk and enjoy the beach!