We applied to go to Argonne National Laboratory's Advanced Photon Source. With a good idea, and a well-written application, we eventually got beamtime for EXAFS (the proposal was resubmitted after it aged). I am currently working up the data and we hope to publish it in one or more journal articles.
If you are trying to find a place to do EXAFS, the best thing to do is email the beamline scientists at the nearest synchrotron that has EXAFS capabilities. They will be invaluable for developing your application.