Nexus 7: micro usb port broken
You did not give details on "broken" in which way, but if it's about not charging,
or having a flaky connection when charging:

There seems to be a common problem with the micro-USB port speciffically in phones.

It is very simple, but not so simple to detect.
The problem is dust on the "back wall" of the connector on the phone.  

If you look into it, wou will just see this "wall", with no dust.
Chances are that there is dust - like fiber collected from cloth of paper in your pocket over time, but perfectly compressed by hundreds of connecting cycles. Looks just like a perfect surface (in the limited visibility situation in the socket).

So please do not make an assumption about it and give it a try - use a needle to scratch that "wall", and see how it reacts.
Next part may be easy, surprising, and fun!

(take care of unpowering the device it you use a conducting tool)