Map of routes
Egypt
Holy Land
Both

If you are taking a reasonably long break in Cyprus, then a mini cruise to the Holy Land, Egypt or both is to be recommended. You can see a lot in 2 or 3 days, and although it is very much an organised tour, it is an interesting one.    You do not have to take any of the excursions at the other end, if you prefer you can wander around by yourself, but for goodness sake don't miss the boat !

You can take a 2 or 3 legged journey, and as you can see by the map both places are very convenient to Cyprus.

There is a two day cruise to Egypt that departs twice a week from Limassol.
On arrival you can be taken by coach to Cairo to see the Egyptian museum, the Pyramids at Giza and the sphinx. Usually a couple of shopping venues are included as well. 

The cruise to the Holy land also departs twice a week from Limassol to Haifa.
Then a coach will take you (if you book it) to Jerusalem and take a guided tour of Golgotha and the Kidron valley, also a walk to the wailing wall, churches, bazaars and
then on to Bethlehem.

Then there is the three day option

It combines both of the other excursions, but mind that the excursion prices are not included in the ticket price. Each coach trip is between C£15 and C£39 (roughly)