The Monastery of St. Barnabas is at the opposite side of the Salamis-Famagusta road, by the Royal Tombs. You can easily tell it by its two fairly large domes. It was built to commemorate the foremost saint of Cyprus, whose life was so intertwined with the spread of the Christian message in the years immediately following the death of Christ. http://www.cypnet.co.uk/ncyprus/city/famagusta/stbarnabas/index.html

The Byzantine Museum at the church of Agios Lazaros (Saint Lazarus) is housed in some of the cells of the hypostyle porch that still stand to its south. The museum’s exhibits include important religious icons, artefacts and relics, including Byzantine icons, gospels, crosses and other ecclesiastical treasures from the whole district of Larnaka. http://larnakaregion.com/directory/product/ecclesiastical-museum-of-st-lazarus