The Rex is old (it used to be the Bachelor's Officers Quarters and temporary home of Colin Powell) but it is well located in the heart of things and as was mentioned elsewhere the roof bar is good fun. Go to the Central Market and if you are coffee drinkers, definitely buy Viet coffee - imho some of the best in the World.

Money being no object (your comment) it would be terrific to get up to Hanoi which is a much more pleasant city. Great French food, vibrant art community and the people are very hospitible. I very much prefer Hanoi to HCM city.

If you do stay in Saigon - do be alert for pick-pockets, purse snatchers, etc.
The old motor scooter snatch trick is very common. 2 on a scooter, 1 drives and the other snatches.

Enjoy, bb