Following up on Joachim Pense’s answer:
Modern Hellenic languages
If we include modern Hellenic languages, a (purely subjectively) ranking of the “outlier” dialects by closeness to Standard Modern Greek is:
- Salento Griko
- Calabria Griko
- Silliot (spoken in Sille, near Konya)
The dividing point for mutual intelligibility is probably Pontic, definitely by Silliot. Of course, it’s not routine practice to consider anything but Tsakonian a distinct language.
Historical Hellenic languages
If we instead include ancient Hellenic languages, traditionally it is considered to be Ancient Macedonian—based on the Hesychian glosses, which have radical sound changes. The recent epigraphic finds OTOH look like routine Doric.
Outside Hellenic languages
If we exclude Hellenic languages and if we trust lexicostatistics, the closest language is Armenian. (See: Graeco-Armenian)