How do i tell if a ring is "Pristine", or not?
Look in the System Map. Select the planet in question, then go to the "Info" tab on the left column. At the bottom of the planet information, it will say "Pristine reserves," or "Common reserves," or sometimes "Depleted reserves." Then it will list information about each of the rings; you want one of the rings (almost always the A ring, the first one and
closest to the planet) to be "Metallic."
Here's a screenshot from a system showing how that info appears:
http://imgur.com/xfzI5S2
I second Simpleye's recommendation of Jura. It has a station not too far away from the pristine rings, and if you get bored with mining you can easily switch to doing some bounty handing in the hazardous RES or do some Empire-affiliated missions. It's all good.
Otherwise, the CIMA prospectors maintain
a database of pristine metallic ring systems, and you can find the closest ones to you.