If you are thinking of the Paphos area, I can recommend
http://www.apollonia-apts.com/ these apartments are all holiday lets and are about 5 - 10 mins walk to the main restaurants and bar street, there are also restaurants within 2 mins!
I can also highly recommend this company, they have apartments (private let) in areas that are walking distance to everything, some are near Tomb of Kings
http://www.cyp4u.co.uk/prop_details.php?id=alina
We have stayed in apartment Kelly which is on the same complex as Alina, its walking distance to supermarket, restaurants, we can walk to the harbour area and it's near the bus route. They have quite a variety of places and really look after their clients.