Which camera Raw will work in Elements 11 that support my new Canon  G1 X Mark II?

You need camera raw 8.4, which is not available to PSE11, only with PSE12 (with update).

You can either migrate to PSE12 or use the free Adobe DNGconverter.

Camera Raw plug-in | Supported cameras

FAQ: Will Photoshop Elements work with my camera, or Why won't my raw files open?

There will be full support for the G1X.2 in ACR 8.5, or so says the release notes for the ACR 8.5 release candidate at Adobe Labs; however, PSE11 stopped being updated last fall when PSE12 came out.  It remains to be seen whether PSE12 will get the ACR 8.5 update sometime in June or July, or if you’d have to wait until PSE13 comes out in Sept/Oct.

The alternative is to use the free DNG Converter 8.5 to convert your raw files to DNG format, which will work in the older ACR plug-in in PSE11.

The DNG Converter 8.5 will eventually be available here:  http://www.adobe.com/downloads/updates however for now you can use the release candidate available, here:  http://labs.adobe.com

Adobe’s supported camera list only shows preliminiary support for the G1X.2 so waiting for DNGC 8.5 may be wise.

You could install canon DPP which comes with your camera EOS disk. Convert your CR2 files to tiff and edit in PSE11.