"I want to be closer to you."
Translation:Chcę być bliżej ciebie.
Closer than you is a comparison sentence. Russian has two constructions here, like: Я младше тебя or Я младше чем ты. The first one doesn't exist in Polish in this meaning, in most situations it wouldn't make sense - "młodszy ciebie"? what does it even mean?
Incidentally, this construction would make sense here, but with a different meaning: exactly "closer to you". I guess it's just that "bliżej" takes Genitive, simple as that.
"к" existed as "ku", but it's rather rarely used, it's dated. It mostly denoted direction (like in Russian), "ku tobie" (Dative) would also only mean that I am going towards you, I think.
So in my example, the Polish would be bliżej niż ty?
The differences in how Russian and Polish have evolved are just as interesting as the similarities.
Just like ku is outdated in Polish, the verbs "to be" have fallen out of use in Russian: jesm', jesy, jesť [still used for emphasis and for all the conjugations], jesmy, jestie, suť
It seems as if Polish uses ciebie in many instances for both the Russian tiebie and tiebia, even though Polish has its own tobie. Analogous to that, Polish also uses mnie for both the Russian mnie and mienia. This is why the word do shows up so frequently in Polish, compared to Russian