Nuclear research and nuclear medicine produce relatively small amounts of radioactive waste.
From the moment radioactive isotopes arrive in our hospitals, universities and research laboratories they are decreasing in radioactivity as a result of spontaneous radioactive decay. The rate at which they decay is described by the half life of the radioactive isotope. The smaller the half life the faster the decay.
Organizations which import these radioactive isotopes have the expertise and equipment to manage and monitor them; if they don't have the expertise and equipment then they shouldn't have the isotopes. This includes storage facilities for the isotopes and for the waste.
So long as radioactive isotopes are used then, irrespective of whether or not governments build centralized radioactive waste stores, these on-site stores will be needed.
Because of the radioactive waste produced when radioactive isotopes are used, and because producing and handling radioactive isotopes is a health hazard, then the decision to use radioactive isotopes in research and medicine should be based on a careful assessment of whether or not there is a net benefit to the community.
Greater technical detail can be found on this topic by searching through
the listed briefing papers and education resources at
http://www.ccsa.asn.au/nic/.