So you are a traveler with very limited time in your hand and can't spend more than 4 days in Egypt. Here are some  things that you should look into that will still give you a great flavor of Egypt without feeling like you are missing a lot.  

There are two places that  you can give a miss - first one is Alexandria - this is a COMPLETE disappointment.  The new library is just a modern building and doing a trip from cairo to Alexandria for just that is useless. While the catacombs are worthwhile - a trip to Alexandria  just for that will be a collosal waste of time.   Mohamad Ali Mosque can also be skipped  as it only eats up time that you can spend in Cairo museum.  

 If you can allocate 10 days for Egypt that would be more in line as there is a LOT to see.

Day 0: When you arrive at Cairo,  stay somewhere near Giza (not near museum). It takes a solid 50 minutes to get to Giza -but the advantage of doing that is the next day you can start bright and early and checkmark one of the biggest line items you came to Egypt for -> Pyramids at Giza.  

 Day1: The Pyramids, Memphis and Saqqara on Day one. Gives you a good idea about how pyramids came to be and goes through the old to new kingdom.  One may stay near Cairo Museum at the end of Day 1.  

Day 2: All day at Cairo museum (take 1/2 day just to walk through the treasures form TutenKhmon's tomb.   In the evening, go to Khan Khaleli -just to experience the bazaar. Please note that because tourism has been hit bad -not all the shops are open now.  In the evening -check in to a hotel that is nearby Cairo airport. 

 Day 3:   Take the first flight out of Cairo ( 6 AM or so) to Aswan. Once in Aswan -head out to Abu Simbel for an all day visit. Stay overnight in Aswan. 

Day 4: Drive from Aswan to Luxor early!! (as in real early). take the day tour in Luxor that covers Valley of the Kings ( and visit the Tutenkhmon tomb and the mummy here - instead of visiting many mummies in Cairo museum), Queen Hapchepsut temple,  Temple of Karnak and Temple of Luxor.  I suggest that you spend very less time on Hapchepsut (as it is mostly reconstructed) and redirect more time to Karnak. This WILL be a LONG day. Stay that night in Luxor as it is unlikely you are going to be able to fly out.

Day 5: Fly out of Luxor to Cairo for your final destination.