@fukubo Let's meet at the café at 13:30 of July 2nd. this sentence is well written. (2) Let's meet at the café at 13:30 on Saturday of July 2nd. both of these sentences are quite appropriate but it depends on the context. is that for a render vous / a meeting with a professional? or to meet a friend? it sounds formal for me.
@fukubo Further to my comments above, I see no reason to change the general structure of either sentence. They are neither too formal nor awkward-sounding, even for informal speech, such as setting a date with a friend.