I just retuned from a two-week stay in Cairo. I would say that it would extremely exhausting to try and do Luxor in one day. I did it last year (I travel there for work 2x yearly) and if i had the opportunity to do it again, I'd choose to stay overnight.
This past trip, I took an excurision to Alexandria via train and it was not as tiring as the Luxor trip. We saw some of the things there, but then again since you have a short time - I'd focus on the Cairo area. The things you shoud not miss would of course be the Pyramids, the Citadel, the Khan el Khalili (I hope I spelled it correctly). The Khan is a shopping area and can be quite touristy, but you have to see it.
I would contact a travel agency as someone previously mentioned. Or if you want, I have the numbers of a few taxi drivers that do tours around the city and can take you anywhere for very little. You could contact them prior to departing for Cairo and get some ideas on things to do. Let me know if interested.
Good luck with your trip plans!!!!