Sure, that sounds like an exciting trip combining culture, history, and beach relaxation. Here are some travel tips for you:

Best Time to Visit:

Limassol & Paphos:
The best time to visit Limassol and Paphos, Cyprus, is from March to May and from September to November when temperatures are mild and there's little rain.

Cairo and Alexandria:
For Cairo and Alexandria, the best time to visit is from October to April. The weather is cooler but pleasant for sightseeing.

Route and Accessibility:

You can find many direct flights from most European countries to Larnaca International Airport in Cyprus, which is not far from Limassol and Paphos.

Order-wise, starting your trip in Limassol, heading west to Paphos and then fly out from Paphos to Cairo. To get from Cairo to Alexandria, you can take a quick domestic flight or a train.

Altitude and Acclimatization:
These locations are at sea level, so there's no need for specific acclimatization.

Accommodation and Booking:
In Cyprus and Egypt, hotels and accommodation match every budget. It's advisable to make your bookings in advance to secure the best prices and availability. Don't forget to ask about airport transfers as many hotels provide this service.

Clothing and Essentials:
In Cyprus, pack your summer clothes, but don't forget a jacket for the evenings as it can get chilly. In Egypt, particularly Cairo and Alexandria respectfully dress modestly due to the prevalent Islamic culture.

Sunscreen, hat, and a water bottle are some essentials you should pack.

Health and Safety:
Ensure you have comprehensive travel insurance. Avoid tap water in Egypt and stick to bottled water.

Local Etiquette and Respect:
In both Cyprus and Egypt, respect local cultures, traditions, and religion. Always ask before photographing people. In Egypt, modesty in dress - especially in religious sites - is important.