In our hotel in Beirut, there were many Syrians on their holidays. It's hard to believe but it looks safe in Damascus. So after the holiday they get back home to Damascus.
Even local taxi in Beirut can get you to Damascus. It's just price question. Regular taxis ask $300-400 for a day trip. You can also get Syrian taxi which goes from bus station Charles Helou under the bridge in Beirut. Or you can get a local taxi to the border and then get a syrian taxi. I got a local taxi for $80 for round trip + Syrian taxi for $100 for round trip from the border or $20 for round trip from the border to Syrian passport control and back. I would recomend a find a good local taxi driver which can barger for you and kind of care for your safety.
Visa. If you need a visa to travel there you still have a chance to get it on arrival. They can call to Damascus fror the aproval. It depends on officers mood, current situation in the city, your passport and stamps there. However it's better to apply for visa in Beirut. I have an australian passport, at first it was ok, then no, then ok again, then he discovered than I was recently to UAE, Kuwait, Bahrain and other countris wich fight for the opposion. If you have it too, it's better to apply in the embassy in Beirut.
If you are lucky enough you'll get the visa and can visit the city. It's just 30 minutes from the border. The driver will drive as fast as he can with slowing down at check points. The driver waves to men at check points. If a car doesn't stop (slow down) at check points, military has permission to shoot the car. There is risk of terrorists or just bandits between the check points. So it's not safe, but to me it looks ok, there are many cars on the road. However there is a risk to be robed, kidnaped or even killed as I've heard. My recommendation is do not travel there anyway.
The city itself looks safe. It has doubled its population during the war. There lots of military on streets of course, but people live as usual: go to supermarkets, schools, work. However you cannot ask locals anything (about politics) without goverment permision.
If you go, it your own risk.
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