I still remember how much fun was to spend the summer with my grandparents. With the grandfather we built hovels, fished and repaired a motobike, the grandmother read fairy tails for us and taught us to milk a cow.
I think it should be based on commonality of interests and freedom of choice - I mean the elders and the youngsters should choose each other. It might a bit difficult for strangers to set up a close contact. These activities should be supported by psychologists and maybe should include some prepared entertainments. It's also doesn't mean that the children have to spent all time with the elderly, they can make friends among fellows in the countryside.