I want a friend that I can just talk to about the things we like.
ご質問ありがとうございます。
justは色々なところに入れられますが、確かに意味が変わりますね。
例:I just want a friend who can talk about the things we like.(「ただ」が「友達が欲しい」にかける)
例:I want a friend that I can just talk to about the things we like. (「ただ」が「話せる」にかける)
例:I want a friend that I can talk to just about the things we like.(「ただ」が「好きなこと」にかける)
ご参考になれば幸いです。