I may come to regret it but it seemed to be the prudent decision at the time. And now.
Basically, Syria is trying to get a bunch of people into Damascus, especially Americans, so they can be a kind of human shield against an Israeli invasion. (Syria is well aware of the Israeli-American friendship and would love to be able to drive a wedge between the two.) I imagine the Americans that go there will end up being full-blown hostages by the time this is done. I'm glad you didn't fall for it.
You may not want to hear advice from someone of my low character, but here it is anyway.
Find a safe place, a bomb shelter if possible, if not maybe the basement of a strong one or two story building, and hunker down. An upscale hotel is always a very good bet, as you would be among foreigners and you would hear the latest developments by word of mouth.
You say you have food and water. I suspect you will find it easier to get out of there in a week or two if you can hang on that long. If you are in Beirut, you aren't in danger of being overrun, but you probably don't want to advertise your presence.