You can definitely have cereal for morning breakfast-quick, easy & inexpensive.
Lunch, you can always have sandwiches. Not sure if you can buy groceries where you will be staying. If you can, that will cut your cost because you don't have to pre-buy & you don't have to carry all the food from home. Lots of inexpensive items, like peanut butter. If you make a roast, save some for next day lunch and add some lettuce as a sandwich. Make paninis with ham & cheese, lettuce & tomatos. Many combinations of paninis. Or just plane paninis with cheese. That's like four lunch days already.
Dinner: Eggs are very easy to make-any way you like and it can be combined with bread for a light dinner. Use your skillet to cook the eggs. Sautee some veggies and have a vegetarian dinner with some restaurant bought rice (you can buy just plane white rice at any chinese restaurant that is very inexpensive).
Whatever you do, DON'T forget to bring salt, sugar, soy sauce, any herbs that you're thinking of cooking with. Or of course you can buy those at the destination. But if you plan on bringing these, just pack them in small containers, they are very light anyways. Be carefull of any liquid-just store in container & put in zip-lock bags for added security.
Good Luck.