We walked about 8-9 kms from the airport to downtown Beirut very early on a Friday morning. We probably could have taken a taxi or minibus but didn't have any Lebanese currency and just a few US dollars so we decided to walk, instead. Besides, we had all day since we arrived at the airport at 6:30 am.
We like to walk and we've walked to and/or from many airports, not only to save money but also to get exercise and see up close what we normally wouldn't see.
As we walked, every few minutes a (mostly beat-up) minibus would pull over to see if we wanted to get in but we just let them drive off without us.
At one point, a guy was filming us from his car. That was a bit unsettling. The guy even followed us for a while but eventually disappeared.
The neighborhoods just north (and east) of the airport are not the nicest but also not the worst. Two weeks later we walked back to the airport to leave the country.