Have any man-made structures mentioned in the Bible been unearthed by archaeologists?

Yes, quite a number of Biblical structures have been excavated. Some of the most interesting are the following:

• The palace at Jericho where Eglon, king of Moab, was assassinated by Ehud (Judges 3:15-30).
• The east gate of Shechem where Gaal and Zebul watched the forces of Abimelech approach the city (Judges 9:34-38).
• The Temple of Baal/El-Berith in Shechem, where funds were obtained to finance Abimelech's kingship and where the citizens of Shechem took refuge when Abimelech attacked the city (Judges 9:4, 46-49).
• The pool of Gibeon where the forces of David and Ishbosheth fought during the struggle for the kingship of Israel (2 Samuel 2:12-32).
• The Pool of Heshbon, likened to the eyes of the Shulammite woman (Song of Songs 7:4).
• The royal palace at Samaria where the kings of Israel lived (1 Kings 20:43; 21:1, 2; 22:39; 2 Kings 1:2; 15:25).
• The Pool of Samaria where King Ahab's chariot was washed after his death (1 Kings 22:29-38).
• The water tunnel beneath Jerusalem dug by King Hezekiah to provide water during the Assyrian siege (2 Kings 20:20; 2 Chronicles 32:30).
• The royal palace in Babylon where King Belshazzar held the feast and Daniel interpreted the handwriting on the wall (Daniel 5).
• The royal palace in Susa where Esther was queen of the Persian king Xerxes (Esther 1:2; 2:3, 5, 9, 16).
• The royal gate at Susa where Mordecai, Esther's cousin, sat (Esther 2:19, 21; 3:2, 3; 4:2; 5:9, 13; 6:10, 12).
• The Square in front of the royal gate at Susa where Mordecai met with Halthach, Xerxes' eunuch (Esther 4:6).
• The foundation of the synagogue at Capernaum where Jesus cured a man with an unclean spirit (Mark 1:21-28) and delivered the sermon on the bread of life (John 6:25-59).
• The house of Peter at Capernaum where Jesus healed Peter's mother-in-law and others (Matthew 8:14-16).
• Jacob's well where Jesus spoke to the Samaritan woman (John 4).
• The Pool of Bethesda in Jerusalem, where Jesus healed a crippled man (John 5:1-14).
• The Pool of Siloam in Jerusalem, where Jesus healed a blind man (John 9:1-4).
• The tribunal at Corinth where Paul was tried (Acts 18:12-17).
• The theater at Ephesus where the riot of silversmiths occurred (Acts 19:29).
• Herod's palace at Caesarea where Paul was kept under guard (Acts 23:33-35).