Regarding the main streets: anywhere in town near Hamra, the corniche, the souk, geymazeh, mar mikhael, etc.
The bar and restaurant scene in Geymazeh and Mar Mikhael is excellent.
As for rooftop bars, I'm not that knowledgeable, however Iris would be one of the top locations.
Also to see, a short taxiride from beirut, are all the restaurants along the waterfront to the North of Beirut. For exemple Punta del Este.
Food? Definitely try a real lebanese lunch/dinner, full of mezze and grilled meat/fish.