In my humble experience, the best places to save some money are accommodation and the choice of the destination.
Saving money on food, as you very well said, is not ideal as experiencing the food is part of the reason you're travelling in the first place. Of course you don't have to overspend every day here, but make sure you try the local stuff in a decent place.
The cool stuff with Airbnb or similar is that you can save money and meet local people, at the same time. In my case this was a great money saver and source of happiness during the trip.