Here is what I posted on the OAT board last July 2010 (see second paragraph on security):
I just returned form the OAT Egypt and The Nile River w/Jordan - Petra pretrip. All of the hotels (including the M/S River Hathor) were very nice. A couple were outstanding.
Note: There is no city wide metro system in any of the cities either country (except in Cairo where there is a subway; however, I never saw any of it). Even if I knew where the Cairo subway was, I probably wouldn't have ventured on it anyway. We always had an armed tourist police guard with us (it did vary dependng on the area; either one guard per two busses, one armed guard on each bus, and one armed guard on each bus and a police car with three more armed guards following the busses, etc.). There were police/security guards all over the tourist sites visited as well as at check points entering the sites. I'm sure there is a reason for this. Which is the same reason that you may not want to wander off too far from the hotel on your own. With that being said, I never felt in danger and/or worried about my safety the entire time I was in Egypt or Jordan.
Belle Velle @ Amman - You really don't have any free time to go anywhere even if you wanted to, both days are full of included activities.
Arma Palace Hotel @ Petra - You can walk a block or so into town; however, there isn't much to see there. I also walked around the block and found a cheap internet cafe here.
Iberotel Cairo Hotel and Casino @ Cairo - This was just a one night stay. There really wasn't much free time here either.
Basma Aswan @ Aswan - There is a (Nubian) museum a very short distance (walk) from the hotel; however, it happens to be part of an included tour.
Steignenberger Nile Palace @ Luxor - In all of my GCT/OAT trips this may be the nicest hotel that I have stayed in. You could take a taxi or horse carriage to the Luxor museum; however, you can also see it on an "optional tour" (which I would recommend doing). Here I did walk across the street to buy some cheap cokes and two blocks (one left then one right) to an internet cafe.
Le Meridien - Pyramids @ Cairo - Also a very nice hotel. There are a couple restaurants close including a Mobil gas station convenience store (On The Run). Every time you walked off the property there were taxi drivers soliciting your business. We did the Evening Sound And Light Show (at the great pyraminds and sphinx) "on our own" by booking it with the concierge at the hotel. It was great and I would highly recommend it. It only cost 130 Egyptian pounds ($23) per person and included pick up at the hotel in a nice van (at 7:45 PM), personal escort to a front row seat, just over 50 minute light and sound show, personal excort back to van after the show, and return to the hotel (just before 10 PM).