At least let me talk to you whenever you're free during the day.
Let me talk to you whenever you're free in the day.
「一日の中」→「During the day, in the day」
「(あなたが)暇なとき」→「Whenever you are free」
「お話させて」→「Let me talk to you」
「At least」→「すくなくとも」
まとめて言いますと、
「Let me talk to you whenever you're free in the day.」と表現します。
「At least let me talk to you whenever you're free during the day.」というのは、
「少なくとも1日の中で暇な時ぐらいお話させてよ」という意味です。