You received the above error because you need to the output of your buffer as input into the Create Spatial Sampling Locations tool, not your drill sites.
The workflow I propose can only really work if you don't have overlapping polygons (buffered drill sites).
I misread your first post. To create the doughnuts, you will need to create 2 buffer outputs (10 and 20 km each) and then use the clip tool to clip/remove the smaller buffer. You will be left with a doughnut. This is what you must use as input into the Create Spatial Sampling Locations tool.
You will then create 1 random point within the buffer doughnut. Afterwards, use Add Spatial Join tool with the "Nearest" match option to link up the original drill sites with the new random points to get the attribute data.
