Would being a captain in the Air Force be looked upon well in grad schools for international relations? Would more direct international relations experience be looked upon more positively?
This absolutely depends on your duties and past experience. Have you deployed? Do you work in some sort of intelligence field, or political aspect? Have you being involved in strategic operations? Did you develop relationships with other military or being part of something like it? Your rank has nothing to do with it. I read a story of how an E-4 intelligence specialist was accepted into Princeton’s Graduate Public Policy program. His rank is nothing special, but his specific view and experience with military intelligence and analyzing in an Ivy League Public Policy class will certainly benefit the classroom.
As you know, some graduate schools will glady take any military vet into their graduate programs. Others, will screen you and see what you have to add to the classroom and the public sector.
If you have absolutely no international relations experience at all, look into easier schools or at least into the program’s Masters in Public Administration/Public Policy programs. Those are similar, but with a different aim in management.
These are my opinions and I don’t have all the answers, but I hope this helps.