The recent implementation of attosecond and few-femtosecond X-ray pump/X-ray probe schemes in large-scale free-electron laser facilities has opened the way to visualize fast nuclear dynamics in molecules with unprecedented temporal and spatial resolution. Here, we present the results of theoretical calculations showing how polarization-averaged molecular-frame photoelectron angular distributions (PA-MFPADs) can be used to visualize the dynamics of hydrogen migration in methanol, ethanol, propanol, and isopropyl alcohol dications generated by X-ray irradiation of the corresponding neutral species. We show that changes in the PA-MFPADs with the pump-probe delay as a result of intramolecular photoelectron diffraction carry information on the dynamics of hydrogen migration in real space. Although visualization of this dynamics is more straightforward in the smaller systems, methanol and ethanol, one can still recognize the signature of that motion in propanol and isopropyl alcohol and assign a tentative path to it. A possible pathway for a corresponding experiment requires an angularly resolved detection of photoelectrons in coincidence with molecular fragment ions used to define a molecular frame of reference. Such studies have become, in principle, possible since the first XFELs with sufficiently high repetition rates have emerged. To further support our findings, we provide experimental evidence of H migration in ethanol-OD from ion-ion coincidence measurements performed with synchrotron radiation.