Seems like there are nasty left-overs from CS5.5 in the registry. Adobe has that Cleaner Tool, but it is intended to solve installation problems only. It might help, but you also might be forced to install CS6 again.
Let's try registry. Assuming you're speaking of INDD files, do following:
- open registry editor (Start menu->Execute->regedit) and open tree folder HKEY_CLASSES_ROOT and scroll down to ".indd" key.
- check the value Standard for being "Indesign.Document"
- scoll further down to "Indesign.Document" and open subkey Shell->Open->Command. The value Standard should show the path to your current ID CS6 exe and have "%1" as argument.
- open subkey Icons->Current version and check value Standard to be "8.0". If not edit it to "8.0" (without quotation marks of course)
- Go to folder HKEY_LOCAL_MACHINE->Software->Classes and perform steps 1-4 here as well.
- Go to folder HKEY_CURRENT_USER->Software->Classes and check if there exists subkey ".indd" and if so, also repeat steps 1-4 here.
Thank you so much.
Whenver you uninstall an older version after installing a new one you remove or damage common files that are required for things to run smoothly, in this case the icon handler .dll file. Doc's suggestion might work -- I've never tried it and I suspect it will not show the correct icon for the version of the files, but the fast way to fix this is to reinstall any versions you want to keep in chronological order.
And I would suggest you keep CS5.5 if you have a lot of files to convert. You are much less likely to have trouble with them later if you export to .idml from CS5.5 and convert that instead of opeing and converting the .indd files directly.