This itinerary is purely indicative - feel free to play around to go to the bits that interest you most! Use the header links for more detailed info and history about each area if you're interested.
Day 1 - Beirut and the surrounding area
Drive along the Rawche and experience the "old Beirut" - take a note of the fun fair that's been there since fore-ever and also the "Hero's Rock" where the Lebanese "hero's" dive to much support (or heckling for cowards) from the passers by each year.
Somewhere along the way, have a Zaatar croissant for a snack with some Jallab drink
Visit the rebuilt Old Town which is called "Solidere" - have a good walk around.
After Lunch - Head to Hamra street which was the main hub of the shopping and see if you can get into the A.U.B. to walk around.
Then make your way over to Ashrafieh and see the sights continuing down to Jounieh.
In Jounieh go up to the top of Harisa (you can cable car up there if you're up to it)
If you are so inclined, head to the ancient town of Byblos ("jbeil" in Arabic) and try and find Pepe's cafe where in the field leading to his cafe by the sea, you can also search for the worlds smallest church! (Clue: Its in the middle of a field)
Then work your way up to Broummana to get the sights of Beirut from up on high. It will also show you how quickly you can go from sea level to mountains in Lebanon.
Head back down to Beirut for Dinner at any of the restaurants you feel like - they are all pretty good. Alternatively, if you can get a booking, try to dine in the old Zouk restaurants
Day 2 - Baalbeck & Anjar & the Bekaa Valley
Visit the old ruins at the temple of Balbeck which is amongst the best examples of Roman temples and the palaces in Anjar. You'll also be in the general vicinity of the Bekaa valey with its vineyards (Chateaus Ksara and Kefraya are both there).
Its a good trek so book the whole day.
Day 3 - Jieta &The Cedars & Beiteddine
The Jieta grotto is a magnificent cavern of stalactites and stalagmites. It is stunning.
The continue up to the Cedars - Lebanon's most prized natural resource. Keep an eye out for the sculpted petrified trees. Cedars are very unique in many ways - more info on this on the Wikipedia reference
Then head towards Beiteddine which is a magnificent palace.
Day 4 - Tripoli
Heading North now - Tripoli is Lebanon's second largest city and is a great place to explore.... they say the best Knafeh is to be found there (irrespective of what Wiki's entry says) and I always found the shopping excellent. Basically you look around and shop a lot!
Another huge day - Sidon is one of the ancient cities and is source of the mussels who were milked for their purple ink that was the staple Phoenician product to ancient royalty and Roman Catholic Church (Only the Pope was allowed to wear the purple colour). Today its hard to see the glory of the old city but if you can - try to visit the soap factory where they still make ancient style soap today.
On the way there - make sure to stop at "Babas" to grab a snack! ;-)
Tyre is another fascinating city with great ruins to visit and a wealth of history.
There is so much to see that you could go on for days... instead I suggest you use this link to get a good list of all the tourist sites and you can pick and choose where you want to go.