During the post-Gupta Era, the university that gained fame was Nalanda. Nalanda was located in present-day Bihar, India. Option 1, Kanchi, is incorrect as it refers to a city in Tamil Nadu but not a renowned university. Option 2, Taxila, is also incorrect as it was famous during the ancient Mauryan period and the Gupta Era came after that. Option 4, Vallabhi, is incorrect as it was a renowned center of learning in western India during the Gupta era but did not gain prominence in the post-Gupta Era. Therefore, the correct answer is option 3, Nalanda, which became famous as a prominent center of learning during the post-Gupta Era.