Tripoli and Tyre

SPDL is absolutely right, these places are calm, it is just their potential for sudden sectarian, camp-based or border fighting which results in such warnings. In the company of locals who speak the language and know the roads, there isn't anywhere in Lebanon I wouldn't recommend. But without locals, getting out of somewhere in a hurry and knowing where to go is more complicated.
All of the south is beautiful, and there's so much to see all over Lebanon. Consider what you'd do if the airport closed on you, then forget about it and have a blast.
ginger beirut

Here's an update: I finally made the trip to both towns and came back alive to talk about it ;-)
There really was no threatening or weird atmosphere in both places. Tripoli really was a highlight, the old town is way more interesting than the other towns I've been to. Military presence was very light in Tripoli, but they are occupying the citadel (which can still be visited).

For Tyre/Sour, I finally made a daytrip on my own from Saida (taxi on the way there, bus on the way back). Having a strong dislike of taxis everywhere, I walked from the Al Bass archeological site to the harbour, thus walking along the al Bass palestinian camp. All the streets into the camp are blocked by army checkpoints, and there were watchtowers and heavy military vehicles on all corners. People were relaxed though, and all they wanted to know was if I wanted to take a minibus to Saida (the al bass roundabout is the transport hub). The old town was so quiet it's hard to remember that this town is in such a troubled area...