Hi,

There are loads of apartments very close the the Plaza in Loz Alcazares. You can find them on owners direct website ownersdirect.co.uk/los-alcazares.htm

Also there are plenty of really nice restaurants nearby in Los Alcazares - we visited 'La Diva' - the steak is about 2" thick and melts in the mouth -well worth trying.
Not an awful lot going on for young children that I saw, but definitely somewhere to visit for an odd night... it is wonderful sitting out for a nice meal in the square watching the aeroplanes come in low overhead with all the lights on - and because Murcia airport is not very big... there are just enough to enjoy watching, without it becoming a noise nuisance.

Also - if you are visiting in September, there is a Roman festival in Cartagena withover a couple of hundred people dressed in authentic costumes parading through the street and re-enacting battles. A must see if you are nearby.