I was there a few years ago, though not to Brasov. Smoking in Eastern Europe - and Romania is about as far east as you can go - is pretty ubiquitous and is tolerated almost everywhere. That said, it's mainly cigarettes they smoke and not cigars. In most bars, smoking a cigar is fine. I don't know about restaurants because I never tried.
Though I will issue a word of caution: smoking cigars in some parts of Eastern Europe immediately identifies you as not only a foreigner but a rich foreigner. You will be the target of hookers and possibly less attractive elements. In other words, don't go into a bar alone, and preferably go with at least two others. I don't mean to overstate the case but you don't really want to stick out much.
Generally, Romanians are pretty friendly towards Americans. However, Americans are easy targets for crime as we are generally credulous and have monney to burn. This leads me to another word of caution: be wary of attractive women in bars who ask you to buy them drinks. Sure you might be getting really, really lucky. But likely its a shakedown and you will be charged an exorbitant price for a special "ladies drink." (I'm talking several hundred USD.) If you refuse to pay after the bartender make this special "ladies drink," you will be either escorted to the nearest cash machine by the bartender and his henchmen, or you will part with a few teeth. Of course, this doesn't generally go on in classy joints or hotel bars, but neighborhood bars or those recommended by the bellman as a true "locals" bar should be approached with caution.
Another thing: beware of Gypsy pickpockets. I know it's not PC to single out a single ethnic group - "pickpockets can be of any ethnicity!" - but trust me on this. Be wary of people invading your personal space and packs of children. Wear a moneybelt and leave your passport in the hotel safe. (But always carry a photocopy.)
Again, Romania is not intrinsically dangerous, but its dangers can be idiomatic and unique. Some of the dangers - being pickpocketed by a woman carrying a baby, for example, or being extorted by an attractive woman at a bar - are mostly Eastern European and not often encountered here, so it makes sense we're not savvy to them.
Then again, nobody in Brasov will likely shoot you for your Nikes...
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