I'm going to third Necker and Chris. Tripoli is worth a visit, but if you've only got a short amount of time in Lebanon, I'd definitely choose Tyre over Tripoli.
Everywhere in Lebanon is easily reachable from Beirut, so I'd personally do something like spend a night in Sidon, a night in Tyre, and then base myself in Beirut for the rest of the holiday and day trip from there. You can either do it independently via serveeces/taxis, or do it via one of the many tourist agencies which are based in Beirut. For the most part, I've only ever travelled independently around Lebanon, though I have gone on one organised day trip from Beirut which was actually pretty good fun and good value - we took in Baalbek, Anjar and the Ksara winery, with lunch at Zahle. The organised trips are a good way to see a lot of things if you're pressed for time.
You really don't want to drive: Signage is practically non-existent, and Lebanese drivers are pretty crazy.