Well General Relativity is a theory of spacetime----the dynamics of it's geometry.
A quantum theory of GR should reveal the fundamental degrees of freedom from which space and time arise---explain how matter interacts with geometry---and say why space is 3-dimensional, or why it is whatever dimensional it is.
that is, a quantum GR should show us the microscopic mechanism from which matter and large scale geometry emerge, and the microscopic context in which matter and geometry interact.
so the primary USE of quantized General Relativity is to answer certain questions like what is space, how does geometric distance interact with matter, what is matter (presumably some wrinkle or kink in geometry.)
the SECOND USEfulness I would say is that quantum GR should stimulate a rebirth of the rest of fundamental physics----by getting particle field theory off of a static artificial minkowski space and getting it reformulated on a dynamic space with quantum geometry.
So whatever particle physics is good for, has been good for in the past---quantum GR should rejuvenate particle physics and make it deeper and more useful---by forcing it to rebuild on a more realistic spacetime (more interactive with matter, less predictable).
So whatever fundamental physics is good for. quantum GR is good for that. It's basic.
However there is a THIRD USEfulness, which is simply to discover how to make small black holes. Small black holes would be a good source of energy, if one could make them out of stuff you didn't especially need. there might be other applications. Louis Crane (University of Kansas physics department) got a grant last year to look into that.
Crane was also going to look into quantumgravity applications to rocket propulsion. Sounds pretty wacky but the point is that you never know what the applications of fundamental science are going to be whenever they finally impact the economic essentials ( energy, communication, transportation, materials,...whatever). It might take a thousand years to get to the really good applications---which is why it seems like a good idea to get busy with the theory.