I would recommend staying somewhere near the Gemmayzeh/Mar Mikhael area. Le Gray is a very nice hotel located a short walk from that area (which, by the way, is full of bars and restaurants to choose from depending on what you like to eat and/or drink). As for rooftop bars, Iris is nice (as mentioned) and you also have Sky Bar. Please have your hotel call in advance for bookings. As an American, you do not need a visa for travel to Beirut (it is granted at the airport - basically an immigration stamp). If you have any other questions, please don't hesitate to contact me. Enjoy your stay.