A bespoke suit for you is definitely a possibility in Athens, yet the required fittings are normally scheduled within a period that might exceed your vacation time. There is rich tailoring heritage in this city and even now that made-to-order is a less frequent request than a ready-made suit, you will find the accomplished specialists to create one for you from scratch or to offer you a great option from their ready-to-wear selection.
For decades wealthy men in the capital of Greece have been very meticulous and demanding with their wardrobe choices, hence the surviving family businesses that are thriving over more than one generation. Tailors in Athens offer high-quality creations based on Italian- and British-inspired pattern-making and using the best of fabrics and materials, at a wide range of price points. You can trust them for custom options as well as for the ones that come right off the rack.
For a list of recommended tailoring options, please see https://www.beyondgreeksalad.com/2020/01/07/where-to-find-a-great-suit-in-athens.