if you enable backup, then root, then check restore when setting it up again, the WiFi passwords should be there.

Thanks Matt--
Please let me know if the following plan of action sounds correct and complete to you.
On my Nexus7 (2012) I have enabled backup to the Google servers and also restore. It allows developer mode and USB connection.  It runs KitKat 4.4.4
I am planning to use the WugFresh Nexus Root Toolkit 1.8.8, as the interface seems understandable to a newbie like me.

1.  I download NRT_v1.8.8.sfx.exe to my Windows Vista computer and run it to install the Toolkit.
2.  Since the Vista computer already runs Android SDK (which includes ADB and Fastboot) and connects to the Nexus7, I assume I won't have to install any drivers.  But anyway WugFresh Toolkit seems to have a Step 3 that will test the drivers.
3.  I'm not going to backup anything to the PC, because the only file I want to save is presumably on the Google backup server.
4.  I connect the Nexus7 by USB and push the "Unlock" button in WugFresh Toolkit.
5.  I click the "custom recovery" box (I don't understand why) and push the WugFresh Toolkit button "Root".
After following instructions, I restart the Nexus7 and enter my account information and ask to restore my files from the Google server.  I am unclear whether there will now be PlayStore apps on my Nexus7 again -- I don't really want them.
6.  One of my apps already is SuperSU (but of course it doesn't do anything right now because my Nexus7 has not been rooted).  I install and run SuperSU (I don't understand this either).
7.  Then, if necessary, I uninstall apps I don't want, and I reinstall apps I want plus other apps that work on a rooted Nexus7.
8.  Now I will be able to find the file I want, which is said to be in /data/misc/wifi, and I can save it somewhere.

I leave the first option in backup and reset checked, back up my data, on all devices. When I enter a password on one it automatically transfers to the others.

Sent from my Le Pan TC1020 using Tapatalk

But the list of WiFi networks on one device is not the same as on the other.  Do you think if I am using Nexus7 (2013) and come to a WiFi network whose password is stored on Nexus7 (2012), the Nexus7 (2013) will mysteriously know the password?

Yer right, just tried on my rooted 2013. Are you using adb from a computer or a terminal app?

sent by mirrorflash Morse code

I am using adb from a Windows computer connected to my Nexus78 (2012)

I want to copy a file from my Nexus7 (2012) before I root the Nexus7.  The file is said to be in /data/misc/wifi, but adb shell won't give me permission for the root data directory and the su command is "not found".  I just want to gain permission to pull a file in the /data directory, or to be a rooted user or a super-user temporarily. Is this impossible to do without rooting the Nexus7?
  The situation seems like catch-22, since if I root my Nexus 7, the file I want will have disappeared.
Any advice?

Is it possible to get rid of the column listing of contacts to the left of the incoming video on a Skype call?  If so, how is it done?

Hi all - first post here after receiving my Nexus 7 for Christmas 

My question is should I update 4.1.2 to 4.2 ? I have read about the problems with 4.2 so should I upgrade or leave it until these niggles are ironed out with the next update ?

Don't upgrade unless you want a particular new feature, such as multi-user access.  4.1.2 was a joy to use but 4.2.1 is very annoying...  slow and unresponsive.  This 4.2 upgrade was surprisingly like a typical Windows update, which normally bloats and slows down a Windows computer.

I had never used an Android device before getting my 8Gb Nexus 7.  I was so confused I couldn't even figure out how to get the lock symbol off the opening screen until I found this forum -- it took me three days to use the N7 at all.  Now I like the N7 so much I am almost fed up with my Windows laptop.  My N7 turns on instantly (from "sleep"), and if I turn on my laptop at the same time I can find out everything I want to know by using the N7 before my laptop has even finished booting up.  Switching from one task to another is also much faster on the N7.

The Kindle app for Android is wonderful for reading books on the N7 and also for PDF files.  If I am not using WiFi I turn WiFi off, and then the battery life is great.  My laptop battery will die 5 times before the N7 battery dies. 

My second-favorite app is Google Drive, which gives me access to all my documents.  And now I find I can save them for offline use also.  Next favorite app is TuneIn for listening to my favorite radio stations wherever I may be.

I am so impressed with the rapidity of updates to apps and to the Android OS.  With my Windows laptop, an update only fixes old problems and slows down the computer.  But each update to Android apps or OS gives me great new features to explore.  I am very happy with the Android 4.2+ multi-users capability.  My wife has her own user name on my N7 and, although normally she doesn't use it, when we are travelling she does use it and so neither one of us needs to bring a computer.

My only complaint is the weak audio.  I have not found any app that will boost the speaker or headset volumes without rooting the N7 (although I have read many articles about apps that say they will boost the volume without rooting.)  I have my fingers crossed that some developer will come up with an app that works.