Hi Yangon style,
Some people told me that they didn't like Mandalay that much either, but I really think there are many interesting things to see there, not specifically in the city but around as well.
I visited Mandalay last November and I did not regret to stop there during this trip to Myanmar.
As John mentioned it, you should really check out the world's longest teak bridge in Amarapura, south of Mandalay. It is really beautiful and you may see many monks wandering around or walking on the bridge. It is even more interesting to be there at dusk as you will see a lot of people going back and force on the U Bein's bridge, with an amazing light.
Sagaing just accross the river is also worth a visit, they have these white and gold stupas you should really go to see and due to the location along the river you have nice views there, especially from the Sagaing Hill.
I also went to Mingun, and the great part of it is not only the riverside village but also the journey to get there, as you get to cruise on the Ayeyarwady river and see authentic bamboo made houses.
When you are in Mingun, there are also a few Paya you could go, but you should really check the Mingun bell, which is the world's largest uncracked bell and weighting about a 100 tons.
If you want to go there I would advise to stay 2 days at the very least in order to visit the city a bit as well as spots around. Things to visit are a bit from each other, and you might be in a rush or even miss many interesting places if you stay too short.
About the Mahamuni Pagoda, correct me if I'm wrong John, but I believe that women can see the deformed buddha, but they are not allowed to be too close. From what I remember, there is an area around the buddha that only men can access and then of course only men are permitted to put golden leaves on the statue, but women can still see it from a certain distance, even if there are indeed screens to show it from a closer point of view.