The Vatican is Catholic specifically, not really all that important to most Christians. As far as Christianity you are looking at places like Bethlehem, Jerusalem and Nazareth, Mt Sinai, really any place that has an association with actual Biblical locations.
There isnt on per se. Not like other religions have. Citys arent Holy anyway. Holiness belongs entirely to God not to lications, dead humans ir inanimate objects. If any city might considered important in Christianity i suppose it would be Jerusalem since Christ and the early church have such close ties to it. But we dont consider it 'holy' as a place to be revered or prayed toward to held up to any particular importance. Our faith is God/Christ centered, not focused on man made cities or objects. The vatican, or pope central, is important only to catholics. It is generally despised, held in contempt or ignored by non-catholics who understand the sacrilege of many catholic beliefs. The vatican isnt important, let alone holy.