Can thoroughly recommend the bakery that Compage shows you.
Try the 'spanakopitas' for breakfast, - fresh, extremely tasty and very filling, oh and very inexpensive as well.
Can also recommend the circular - 'white cheese (tyri aspro I think)' tirropitas, a bit different but again, superb.
Used to take a trip down most mornings, and it was a mission of mine to make the Lady smile - which wasn't easy.
Always spoke and ordered in Greek, she always spoke in English - Marvellous !!
Either way, get there relatively early and you wont be disappointed.
As for supermarkets, can recommend the one that the English couple run, all you need.
The one as you come into Plakias from Lefgoiya is more like a proper supermarket and probably has more variety, but only used that when coming back from a beach somewhere and have the car.
Hope that helps,
Cheers
Neil