You have been given some very good websites for the area, for restaurants also look at
http://puertomarinaowners.com/Owners/Restaurants/Index.html
The area itself used to be devoted to farming and some mining is fairly flat and is not the most picturesque in Spain, though mountains surround you and some of the best beaches are to be found here.
Los Alcazares is not a large or even a pretty town but has a stunning beach and 5Km promenade, great for kids, sailing, cycling,walking. Hotel Encarnacion on the prom is worth a treat, most others bars are beach type bars
Old town has a number of good Spanish restaurants and tapas bars and is centred near to the Town Hall
Newer town is built as a pedestrian precint near to the 525 Hotel and features many different restaurants small shops, banks and bars, more British feel
I lIke restaurant El Patio and Flavours
The main tourist office is near Urb Oasis email losalcazares@marmenor.net also try turismo@marmenor.net
Cartagena is 30 mins away and great place to visit as well as Murcia City if you have a car which I think is necessary
La Manga strip is a little boring, 20Km of high rise buildings but Cabo de Palos nearby is worth a visit as is the national park of Calblanque near La Manga golf resort.
All the towns on the Mar Menor such as Santiago de la Ribera, Lo Pagan and San Pedro have attractions including spas and mud baths and markets but are small
Torrevieja may appeal to some is 30 mins north can be busy depending on time of year
Jumilla is supposed to be the place to visit for vineyards but must be an hour or so away as is the Old Spa town of Fortuna and the mountains of Sierra Espuna are worth a trip.
Get a decent map and guide of the area
Golf in the area is very good but as always, pricey, sailing is superb, in fact the whole area is one of the best kept secrets in the whole of Spain
Hope this helps