いく is the correct one in this case. The reason is as you said, because it's associated with 食べに.
おこなう is a very formal expression that has various meanings when translated into English (such as to do, to conduct, to have, to make etc). You almost never hear おこなう in everyday casual conversation.
However, when it comes to reading, it's true, sometimes difficult to tell which way to read it at first glance.
I would say the keys are
- Pay attention to the particle before 行く/行う.
- Get some hints from the context.
The below are some example sentences where you can distinguish between いく and おこなう by the particle.
調査に行った。（〜に いく）
I went to investigate.
調査を行った。（〜を おこなう）
I did some research.
友だちは今、実験に行っています。（〜に いく）
My friend is going to an experiment at the moment.
教授は今、実験を行っています。（〜を おこなう）
The professor is conducting an experiment now.
The below are some example sentences where you can distinguish between いく and おこなう in context.
彼の指示どおりに行ったので、プレゼンテーションは大成功だった。（おこなった）
I followed his instructions, so the presentation was a great success.
彼の指示どおりに行ったので、全然迷わなかった。（いった）
I went (there) according to his instructions, so I didn't get lost at all.
