There's an implied "in order" between "here" and "to" in English. The Czech conjunction "aby" has that function - to express purpose. There is no way in Czech to simply attach the infinitive here, a side clause is the way to go.
But "going to" is something very different, it's essetially a composed future tense, the literal meaning is gone. "We are going to teach you Czech" will simply be "Naučíme vás česky". If, on the other hand, we used "going" literally, such as "We are going to London to teach you Czech", then yes: "Jedeme do Londýna, abychom vás naučili/učili česky." But in this case, it's also possible to simply use the infinitive in Czech: "Jedeme do Londýna učit vás česky" - although it sounds a bit curt.
Another similiar typical example is: "I want you to come here." -> "Chci, abys sem přišel." (no way to use the infinitive here).