Just a quick note on the directory naming: idlelib/idle_test sounds like a good option to me.

Putting it under idlelib makes it easy for distros to carve it out along with the rest of Idle, as well as making it clear that it falls under the purview of PEP 434

Expanding Itest -> idle_test is a combination of "Itest" being somewhat cryptic in the first place, and then the potential for 1/I/l/i glyph confusion (depending on font) making it worse.

Other than that, +1 to what Ezio said (I wouldn't worry about moving any more existing tests for this patch though - starting to move self-tests out of the individual IDLE files to the new test suite can be a good next step)