Named for the starburst formed by the radial streets of the main square, Place de l’Étoile seems to either be totally empty or rammed with families with children on rented tricycles with attendant uniformed nannies. If your kids don't go in for archaeology, this is a good place for them to run wild. Once a traditional Levantine souq, the stalls and cafes were razed during the Lebanese civil war (like much of the rest of downtown), having since been replaced by overpriced cafes.
The 1930s Rolex clocktower was a pre-war gift from Lebanese-Mexican billionaire Michel Abed. Downtown gets shut in by guards after midnight, but opening hours in the morning are flexible.