Ottoman Turkish was already written in a modified version of the Arabic script, so geographical proximity to other Middle Eastern countries would not have influenced the decision. The decision was based on the script, in that form, not suiting the language. The Turkish variant of the script needed reform - (redundant letters, often consonants and lacking in Turkic vowels).

Just to be clear - there was no doubt that reform was needed. The options on the table were thus: modify the script to account for differences in the language or to create a new script and switch to that.

Advocates proposed a Latin script decades before it was actually implemented. And Ottoman Turkish had been written in Latin for a long time (dictionaries for Balkan languages had both languages in Latin, for example).

At the time, the USSR was undergoing a program of Latinization (as a part of modernizing and standardizing languages, education and so on), so it would've been the strangest time to switch to Cyrillic. The Turkic republics of Kyrgyzstan, Kazakhstan, Uzbekistan and Azerbaijan all switched to Latin, along with all the smaller Turkish languages within the USSR. This gave the reformists the push they needed.

The Turkish script used letters that were already in use by other Latin scripts. ö, ü, ç and ş (possibly.. I did not know until today that the Romanian ș is not the same letter). Only ı and ğ were added from scratch.

The Greek language was not really an option. It brought no advantages in terms of facilitation of technology or trade with the rest of the world and would have a similar problem to what Arabic had. Redundant characters and missing ones. There are dialects of Turkish that were written in the Greek alphabet (Karamanlidika, for example, as well as the Turkic languages Gagauz, Surguch and Tatar) but basing the new alphabet on Greek was not considered choice. Tosk Albanian and Vlach had switched from Greek to Latin, meaning, the only major language that used the Greek alphabet was Greek, to this day.