Westerners I've met in Beirut have a range of attitudes toward current events. Some read the International Herald Tribute (a kind of "world edition" of the New York Times)and take a global approach, preferring to know a little bit about what's happening everywhere. Some are obsessives about the middle east, and Lebanon in particular, and read all the English-language news sites, following each new development. Others prefer to avoid the news altogether; they aren't necessarily cynical as much as critical of the gossipy and sometimes unreliable reports about the complicated politics of Lebanon.
These are the three news sites that our friend at the U.S. embassy recommends:
The Lebanon Daily Star
I read the Daily Star most days, mainly, I must confess, because it's the most user-friendly of the three. The site is informative but I've found you must read the stories there calmly and somewhat skeptically. For example, the Star will report on standard State Department or Embassy memos as if they signal changes in policy. The usual "be careful when you travel in the Mideast" will become "Secretary Clinton has warning for Americans in Lebanon." And for months all three sites have been referring to "rising tensions" over the tribunal investigating the Prime Minister's assassination six years ago--although most everybody you talk to says that tension, insha'Allah, is quite minimal.
Knowledge and awareness are good things, and so is gathering info from a variety of sources, but so too is avoiding alarmism. My impression is that a lot of good people in Lebanon are working to normalize peacefulness. Peace makes a good carrot. It's right there in front of Lebanon, dangling, ready to be grabbed. Although I love the free flow of information, I worry that sometimes the news can be counterproductive. A guy told me recently that when you're used to strife, sometimes the reports about tension create a kind of adrenaline rush. I think there's some truth to that, but, like I said, I'd like to think that peace can be just as addictive.