Translation:I go to the east.
Yes, but a little old-fashioned sounding. Probably something you'd hear in old westerns or any movie trying to capture that style or a "days gone by" sense (i.e., Lord of the Rings), so more literary these days.
The reason "I go to the East" (notice the capital "e") is acceptable English is because "East" is considered a place and can be referred to as a noun.
Roughly speaking, "へ" means "to" in the sense of "towards" or "the direction of," while "に" is more like "to" as in "this is my destination," generally putting more emphasis on where you end up. I suppose you could think of it as a "journey" vs. "destination" distinction. If someone better understands the subtlety, please feel free to jump in.
Also important to note is that "へ" is pronounced as "え" when it is used as a particle.
To speak frankly " I go to the east" is ugly. "I am going East" should be perfectly acceptable along with any sensible combination of "I /we/ he/ she /it" , go, am/are/is going, will go (to the ) East/Eastward should be accepted. Literal transliteration is one thing and may show the construction of the sentence in the original, albeit that "East to go" is plainly ridiculous in English. Good translation is quite another, tasking us with the rendition of the idea of going in that direction, euphoniously in our own language. Confusing the two in such fashion is damnably frustrating and not at all helpful.
The purpose here is not translation but learning. Translation is simply the method we use on duolingo to further our learning of the language. When you learn a language you have to grasp the differences between the new language and your native language. If the new language does not use the same verb form for a continuous verb as for the simple present tense or simple future tense, that is something we need to learn. Even if this leads to less natural sentence structure in the translation, because our goal is to learn and not to produce a translation for use, we should overcome the natural irritatation. So long as both versions of the sentence are grammatically correct and retain the important points for our lesson (the points of Japanese usage) we should have achieved our purpose.