Alexandria, Cleopatra's royal capital, is in modern Egypt. The city stands on Egypt's Mediterranean coast at the western edge of the Nile Delta, making Egypt the single canonical answer.
Alexander the Great founded Alexandria in 331 BC on or near the older Egyptian settlement of Rhacotis. Its position linked the Mediterranean world with the Nile Valley, and it quickly became the leading Greek city in Egypt.
After Alexander's death, Ptolemy I Soter took control of Egypt and eventually made Alexandria the capital of the Ptolemaic Kingdom. Cleopatra VII ruled from there, and the city became famous for its library, scholars, harbor, and Lighthouse of Alexandria.
A common mix-up is confusing Cleopatra's capital with Rome, where she had political connections, or with cities named Alexandria elsewhere. There are many Alexandrias, but Cleopatra's city is the Egyptian one. After the Ptolemaic dynasty ended in 30 BC, Alexandria remained a major Mediterranean center for centuries.