We take a cooler bag with just a small bit of chedder and some bacon to start off with then just buy the bits we need out there. I do take tea and coffee too. You can get a bit bored with Laughing Cow cheeses, but try some of the local cheese, you dont need a lot for lunches. You can get wonderful tomatoes etc and whip up an omelette in next to no time for lunch or some local sardines, glass of wine, olives and bread - on the balcony fantastic! Some times we just have a banana and some crisps on the beach and head back for snacks and local wine after a dip in the pool & then have dinner later on. Other times we have just had pasta at the accommodation and then gone out for drinks and desert later. Depends on what your taste in food is really and what you cannot live without for 2 weeks.
Last year we went on an extremely long walk and even though we had water we had no food. We popped into a tiny shop in a village bought a lump of very tasty local cheese which was cut up into strips for us for convenience, a banana and some chocolate and we were set up for the long walk back and then had a welcome ice cream.. good memories!
I have heard there is a Lidl just outside Corfu town too, not that I have seen it.