We live in Cyprus having moved here permanently from the UK in 2004 and have travelled to Egypt a couple of times independently from any tour operator or local agent.
Flights go on more or less a daily basis from Larnaca airport to Cairo with Egyptair and you can book directly online with no problem. The flight departs around 7.30pm arriving in Cairo approx 90 minutes later.
I would recommend spending 2 nights bearing in mind your first night would be the evening of your arrival.
As an example, I just costed up return flights for 2 people on Mon 21 March and returning to Cyprus (LCA) on Wed 23 March and the cost came up at 248.06 Euros total for both passengers - not per person.
Remember, Cairo is a city and city accommodation costs are generally higher than in a holiday resort. The same applies here if you compare Nicosia hotels with something in Larnaca or Limassol but we've often found some good accommodation deals for Giza and surrounding areas on Travel Republic, Sunshine and Thomson websites.
We've also taken Salamis and Louis Cruises (2 and 3 day trips) from Limassol to Lebanon (Beirut) and Syria on a number of occasions. They are extremely well organised and you can pre-book excursions at the time of making your online reservation.
You can also book directly with Louis Cruise offices and there is an office in each of the main resorts of Limassol, Paphos and Ayia Napa.
If you book at last minute (within 48hrs) you will get any discounts or upgrades as available.
If you book with them directly in advance and a special offer becomes available closer to the date, they will either reduce the price or upgrade you.... You will not get that kind of offer if you book with a tour operator or agent.
If anyone wants any help or info, I'm happy to oblige. We generally book another flight onwards from Cairo to either Luxor or Aswan and internal flights are very cheap. We've done Cairo several times in the past and now tend to go to Egypt as a holiday destination. With flights being only around an hours' duration on each leg it's a simple and pleasant trip for us from Cyprus.
Cheers
Shell,
Limassol - Cyprus