I highly recommend the visit of Campo Santo Teutonico - the German Graveyard - just on the left side of St. Peters: even in hot summer it's wunderful shady place, very calm and serene, and still on state of Vatican City. You need to go through a security gate, but it's not very much visited, so no lines of waiting... But beware: It's a real graveyard, still in use, so please behave yourself and don't party there ;-)