The American University of Beirut's archaeology museum is the third-oldest in the Middle East, founded in 1868. Tucked inside Post Hall on the AUB campus, it holds a tightly focused collection of objects from the Levant — flint tools, painted Phoenician pottery, Roman glass, and a beautiful set of glazed Islamic ware.
Entry is free, the rooms are small and well lit, and the visit takes an hour. Combine it with a wander around the AUB campus itself, which has manicured gardens and one of the best Mediterranean views in Beirut.