Do not go to Sham. It is a rat hole full of Brits. What is the point. You don't need a visa to visit Sharm, which is a bonus, but it does mean you won't be able to leave the immediate area and go on a tour.
Hurgada is still touristy, but at least you are able to go other places (not that there is anything nearby).
We go every year (g.f an archaeologist) so suggest Luxor. It is on the Nile, it is a big city, lots of history (Karnak, valley of the kings, luxor temple et cetera) and really caters for all one's needs. Lots of regular cheap flights.
We once stayed on the private island hotel called Jolie Villa, which is very pleasant but away from the hubbub.
Unless you want a holiday full of lobster red drunk Brits... then Sharm ;o)