Well, Baalbeck is worth seeing if you can get there - it is in the heart of Hezbollah territory so if you go, go with a local who can interpret what is going on. Otherwise Anjar - an Armenian area has similar ruins.
Just to the north of the Madhaf (museum) crossing from east to west just off a major north south road (and I can't remember the name of the road) but near to a statue of Camille Chamoun they have left a couple of bullet chewed buildings of you want to see what large areas of the city used to look like.
The area rebuilt on Martyr's Square is in a beautiful honey coloured stone and thetre isa very pretty mosque there.
Maybe catch the cable car (telefrique) from Jounieh up to Harisa, reasonable views as I remember but probably changed now with so much building going on.
Byblos, a very pretty little port with great fish restaurants around the port (and I don't even like fish!) expensive but you won't eat there every day. Good Roman and crusader ruins there too.
A very good little local Lebanese restaurant off the sea end of Hamra street in West Beirut, I'll try to find the address. Tiny and good food reasonably priced.
Really you should go to Syria and/or Jordan if history is your thing, great castles and roamn ruins in both countries.
There's a crusader castle to the right of the road as you go north from Beirut before you get to Chekka, I don't know if you can visit it though.
If you visit Geita Caves by Jounieh (where the Christians stored ammo during thre civil war) the top cave system is way more impressive than the bottom one which you visit by boat and if you are pressed for time is kind of dumpy compared to the top caves. Nearby at Nahr alCaleb (Dog river) you can see the plaques carved into the rocks by Napoleon's troops.
81-85 was fascinating, not healthy but fascinating.
Edit: I'm sure there will be some passanger ferry traffic from Cyprus to Lebanon, or you'd be able to go on a cargo ship but the thing to do would be to go to Cyprus and look/ask around. If you don't have a lot of time you may spend several day doing this so I guess flying would be the best bet.