Depends where you are intending to visit on Rhodes. Lots of tourist type supermarkets in most of the resorts and also some larger supermarkets in the larger towns.

I think you'll find everything you want in the larger supermarkets.It's changed dramatically over the past few years and there's a good selection of British names as well as Greek on the shelves.

We have been S/C in Faliraki on & off for 15 years. Never had probs. using the Supermarkets for tourists.Fresh fruit & veg can be bought @ the Saturday market outside Rhodes Town.

And don't forget Marks & Spencer in Rhodes Town.

There is Lidl on the coast road toward Rhodes (before the fruit and vegetable market). There is Spar and Marinopolos nearby, all very good Supermarket. On the main road to roads youwill find AB in Faliraki, another Lidl and AB. For the big supermarket you need a car or something, but it is worth it, as the tourist supermarkets are much more expensive.