Shoes in greece

Either would work. The most important thing is shoes with a good tread and food support to help prevent slipping and falling. If you go when it's hot, I'd lean towards sneakers. Also, if you are not checking a bag, hiking shoes will weigh more (of course you could wear them on the plane.)

When and where exactly?

I think it depends on your feet. I always wear light weight hiking shoes which have more support and traction than sneakers. We were just in Greece and our late twenties son and his wife wore sneakers. I wore sneakers in town but preferred hiking shoes for uneven surfaces.

Where are you going and what are your planned activities? Hiking in the mountains of Meteora is a lot different than same distances on streets and hills of cities, sightseeing. I mostly wear my Teva hiking sandals, but that doesn’t mean it’s the right choice for your age and activities. (Nor are they the right choice for me 100% of the time.)

In Greece, I mostly wear lightweight hiking shoes, they’re versatile and they work well for any situation. You can even keep them on for evenings out in Athens if you don't have anything else to wear.

I have pairs from Merrell and Columbia, lightweight and waterproof. Something like this:

https://www.columbia.com/p/womens-tellurix-titanium-outdry-shoe-2148911.html

Or

https://www.merrell.com/US/en/wrapt/50939W.html?

I wear and bring only one pair of quality hiking/walking shoes suitable for flat, hilly terrain or just wandering around like JoLui posted.

No need to bring multiple types of shoes that adds weight to your luggage.

My go to shoes for Greece, Spain, home, wherever are the Merrell Vapor Glove barefoot shoes.