We have done the 3 day trip by ferry with Louis cruises to Lebanon & Syria (before they started fighting) and then the year after we took the 2 day trip to Lebanon.
We really loved Lebanon - great ancient site at Byblos and fantastic shopping for throws, shoes & gifts in the market there. You also get to visit the stalagmites & stalactites in the grotto, the church of St Mary perched high on the hillside and then a tour of Beirut centre (guided) with some free time to wander round the shops. The shopping is good and the centre of Beirut is very mediterannean - some of the buildings are very Italian looking.
Syria - we missed getting on the excursion to the fortress "Craque de Chevalier" and we will certainly go back again.
Much cheap Duty Free shopping in the Cyprus port and even better in Lebanon ports. Nobody stops the tourists coming through the Cyprus customs at the port on your return as they are too busy targetting the Cypriots as they are notorious for their "shopping" sprees....