What does the following phrase that I heard several times in central Greece mean, “tha paw na koitasthw” (“θα παω να κοιτασθω”)?

Dimitris Sotiropoulos reports in his answer that in some areas of Central Greece, this means “I will go to bed”. The normal meaning of the verb in modern Greek is “to look”, but the current accepted etymology of the verb is indeed from an ancient Greek verb for “to lie down”. This was not always the accepted etymology (it’s not terribly obvious, after all), which is why the verb used to be spelt as κυττάζω rather than κοιτάζω.

Dialects are often repositories of archaism, of course. In Cretan, “to lie down” is θέτω, a remodelling of ancient τίθημι “to set” — the meaning the verb was revived with in standard Greek.

OP’s expression will remind most Standard Greek speakers instead of the idiom να παίζει να κοιταχτείς, “you should go and get looked at”. Meaning “you’re crazy”. (The person who implicitly will do the looking at you is a psychiatrist.)