One thing for sure is that it is a very different place than in the 80s when you were likely to be hit by mortar fire.
Things have gotten better, but in all seriousness, many countries situations can change quickly.
The best advice is to tune into government web sites and travel advisories, then do whatever additional due diligence is wise.
Here is your US site
https://travel.state.gov/content/travel/en.html
The latest state department warning was updated in December.
Sometimes the updates are for the better and sometimes for the worse
When they contain generalities, it means act wisely.
When they are specific, there is something more likely to occur.
Dec 2015
https://travel.state.gov/content/passports/en/alertswarnings/lebanon-travel-warning.html
You can also gain perspective by checking other countries advisories (Britain or Canada for example)
Now, having said all of that, just like a Canadian travelling to the US, there are parts of a city or country to be aware of and avoid.
I use the Canadian US example, because we aren't used to worrying about wondering off the beaten path into trouble areas, and it is something I've had to learn about US cities. For you travelling to foreign cities it is similar though the risks are different, some areas are ok and some are to be avoided. Our Canadian advisory breaks it down by areas to be particularly avoided versus taking arise but being vigilant.
Here is Canada's most recent
Click on the security tab for more specific advice
Travel advice and advisories for Lebanon