Option 1: Nikitin - Nikitin was a Russian merchant who traveled to India during the fifteenth century. He did not visit the Vijayanagar Kingdom and was not from Italy. Therefore, option 1 is incorrect.

Option 2: Fa-Hien - Fa-Hien was a Buddhist monk from China who traveled to India during the fourth and fifth centuries. He did not visit the Vijayanagar Kingdom and was not from Italy. Therefore, option 2 is incorrect.

Option 3: Bernier - Bernier was a French physician who visited India during the seventeenth century. He did not visit the Vijayanagar Kingdom and was not from Italy. Therefore, option 3 is incorrect.

Option 4: Nicolo Conti - Nicolo Conti was an Italian merchant and explorer who visited India during the fifteenth century. He is known to have visited the Vijayanagar Kingdom during his travels. Therefore, option 4 is the correct answer.

In conclusion, the correct answer is option 4 - Nicolo Conti, who was from Italy and visited the Vijayanagar Kingdom in the fifteenth century.