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You are not supposed to install the module separately. Doing so will ruin the Joomla! database due to API changes between Joomla! 1.5 and 1.6. What you have to do is simply install Akeeba Backup 3.2.b4 or later on your Joomla! 1.6.0 site and the module will be installed automatically. You may have to enable it manually, though.

You can set its position to "icon" so that it get published in the correct place. Do note that, unlike what used to be in Joomla! 1.5, administrator icon modules are published in sliders below the main Joomla! icons. Look at the interface very carefully. You'll see that below the Joomla! icons there is an "Akeeba Backup Notification Module" header. Click on it and the icon will be revealed. No, you can't change that. No, it's not a bug. It's how Joomla! 1.6's default administrator template (Bluestork) works. I don't like it either, but we'll have to live with that.

The Joomla! interface has changed a bit. OK, it has changed a terribly whole lot! Here's how to do it:
1. Log in to your backend
2. Click on Extensions, Module Manager menu
3. The top row above the grid has an edit box and, on the right, a series of dropdown boxes. The first one reads "site". Select "Administrator".
4. In the Filter text box type "backup" and click on the Search button next to it.
5. Click on the only item, titled "Akeeba Backup Notification Module"
6. In the editor page, find the "Position" setting. It's the third setting on the left-hand pane. Click on the "Select Position" button.
7. Find the "icon" setting (sixth item from the top for me) and click on it.
8. Back to the editor page, set Published to "Published" (yeah, I know...) and Access to Public.
9. Make sure that Start Publishing and Finish Publishing are both "0000-00-00 00:00:00"
10. Make sure "Language" is set to "All"
11. Set "Show Title" to "Show". IMPORTANT! If you don't do that, you won't see the icon!
12. Save & Close

Now go to Site, Control Panel. Right after the "Edit Profile" button there should be a "Backup required" or "Backup up to date" icon (depending on the age of your backup).

Do note that installing 3.2 Stable (to be released probably tomorrow) on a site where Akeeba Backup and its module is not already installed will do all of this automatically. The current beta version didn't because the way modules work has changed a gazillion times during the beta releases of Joomla! 1.6. We had to wait for it to go stable before figuring out how to make everything work properly.

Yes, you are right. There were a lot of UI changes in Joomla! 1.6's default administrator template, all performed without any user testing whatsoever. Good thing us third party developers decided to support the new Joomla! version and help fill in the gaps in the documentation ;)