What a coincidence! I just read an essay (actually it's a comic strip) on this subject. In that book it says, "へ (e)" implies a direction to a destination while "に (ni)" implies a particular point of destination. In this context, "へ” can also be expressed as "no hou e （の方へ）" and "に" can be replaced with "made (まで)". For example, we can say "higashi e ikimasu" but cannot say "higashi ni ikimasu" because "higashi" (east) merely indicates a direction but not a place. Please be noted that I just quoted the essay so this is not my original idea. I sort of agree with it though.

When I teach Japanese I explain it like below 1. I go to the bank. ( ginkou he iku) 2. I go to the bank. ( ginkou ni iku) ....? the same??? but wait. example 1 is the simple form of the sentence. and what about 2? This sentence has some `hidden words` in the sentence. I go to the bank (to withdraw some money). -> ginkou ni (okane wo oroshini) iku. I go to the bank (to meet my friends). -> ginkou ni (tomodachi to aini) iku I go to the bank (to deposite some money) -> ginkou ni (okane wo azukeni) iku Thus, When the sentence was used "ni", it is implying to have another/other purpose(s) to do in the bank. If you are mentioning to just go to the bank, and thats your purpose, you can use *he*. But usually people dont think about those rules too much. They just use them randomly. And there are some exceptions too, but those have already been explained by Takashi earlier. Using *ni* as *to*, and *he* as *for* in English.

Just in addition to the good answers above, I use "ni" more often than "he" in daily conversation. On the other hand, I tend to choose "he" when I write formal essays. Everyone has difference speaking/writing style, though, of course.

Nothing.