Wiki), but last two weeks of June we managed to get there and enjoy some fabulous time.
The weather is pleasant on that time of the year and by far not so hot as it will became in July and specially in August. Actually it was already quite warm and the sun was getting more agressive every day.
The place is a refugee for families with kids and people with a lot of time to spend doing nothing as due to it peculiar geography everything is far away. So, basically either you go nowhere or you use the car all the time.
There are some small shopping malls along La Manga and several supermarkets, so you will never run out of supplies. The idea is to go there to a rented apartment or to a hotel for a shorter stay and enjoy the beach and the sun.
Close by is the city of Cartagena (Wiki) which is a nice place to visit, full of history and naval tradition including the original submarine build by Isaac Peral y Caballero (Wiki), probably the first modern submarine.
However, one of the best discoveries for us was an Italian Ice Cream shop, owned by an Argentinian couple called New Bo (Web), which probably has one of the best Ice Creams in the area as the owner has been in Italy and has learned the traditional Ice Cream making there. Really worth a visit :)