Frist time I've heard anybody use Tokyo as an example of cities with cheap housing.

Desirable areas of housing in Houston are only cheap relative to SF area, downtown Portland, and downtown Seattle. Plenty of million dollar condos in Houston, and a nice but small one bedroom/studio in a good part of Houston start at about $1500 a month.

It does appear to be easy to build here, though. Tons of new high density residential being built, but it's not making the prices come down at all.

You're using a very unusual definition of "relatively cheap".