How do you store all return values from a while loop in a vector in matlab ?

You can just store it as a vector:

 vector_choice_breakfast  = cell(1000,1);
 count = 1;
 while breakfast_choicerep == 'Y' | breakfast_choicerep == 'y'

    choice_breakfast = menu('What do you eat for breakfast?',breakfast_items);
    vector_choice_breakfast(count) = choice_breakfast;
    count = count + 1;
    breakfast_choicerep = input('Did you eat anything else for brekfast? (Y/N): ', 's');
end

The only issue is that you have to make sure you handle what happens when more than 1000 breakfast items are eaten, which could involve throwing an error and handling it (say by resizing the vector) or simply disallowing more output.