You only have one day to see the Museum, the Khan and either Islamic or Coptic Cairo? WOW! That is going to be a fast paced tour. Can you get another day in Cairo for this?

Both Islamic Cairo and Coptic Cairo have some wonderful old buildings from as far back as the 900's. If you have no preference of your own due to religious beliefs or whatever, then my vote would probably be for Islamic Cairo, but try to see something different or more than JUST the Mohamed Ali mosque (in the Citadel) which isn't very old or as interesting as many of the others IMHO. Try to get to Ibn Taloon, Qait Bey, or any of the monuments on El Muizz Street.

Thank you. We do have a day at end of our tour as well, but no guide for the day. Any suggetions for us?

The Museum itself can take a full-day. So consider this when planning other stops during your time in Cairo.

Debbies suggestions are ideal, but scheduling is important.

Unless you are very comfortable on your own by the last day, you might want to hire someone to take you around that day as well and fit in some of the unseen sites before you leave. There are hundreds of things you can see on a day off like that. You could head out into Islamic or Coptic Cairo, or get out of the city and do something in the Delta or take a drive out to the Suez Canal, or take a Cooking Class, or more shopping - lots and lots and lots of things to do.

Don't be afraid to hire a Guide for that last day. A good Guide is definitely worth the extra cost.
By the way, if you are at all familiar with this Forum, you should know that Debbie (Casual Cairo) is one of the best Guides in Cairo. I would strongly suggest that you contact her.
Have a great trip.

A second vote for using Debbie (Casual Cairo) of Casual Cairo Detours.