Final answer:
The most famous and cosmopolitan Hellenistic city was Alexandria in Egypt, known for its vast population, vibrant mix of cultures, and significant cultural institutions like the Museon and the Alexandrian Library.
Step-by-step explanation:
The most famous and cosmopolitan Hellenistic city was Alexandria in Egypt. Founded by Alexander the Great in 331 BCE, it became the capital of the Ptolemaic Kingdom and was known for its cultural and scientific pursuits with the establishment of the Museon and the renowned Alexandrian Library. Alexandria's population reached one million and exemplified the Hellenistic era's blend of Greek and other cultures, including Jewish communities from Palestine, making it a vibrant center of diversity and learning.