I wish to land in Japan looking for eikaiwa work. In which city are 
opportunities best for attempting to find a job? My only qualification 
is a degree.

I have narrowed it down to those two. Tokyo because it's sheer size 
presumably brings opportunity.

And Nagoya because it might be less flooded with gaigin (Kyoto is said 
to have a glut of gaigin seeking those jobs because they are attracted 
to the city for whatever reason - surely Nagoya would be the opposite?).

Also the economy there is booming with the lowest unemployment in the 
country.

Or are eikaiwa jobs so scarce these days that neither is realistic?