The particle e へ, pronounced as "e" despite being written with the Kana glyph for "he," is essentially interchangeable with the particle に for its single usage in Modern Japanese, but its interchangeability is heavily stilted in favor of に.
The reason for why it is written with へ as opposed with え is because it actually comes from the noun 辺（へ）, not to be confused with the synonymous Sino-Japanese hen へん written with the same Kanji. へ is not used in isolation to mean "location/area" as a noun, but it can still function as a noun inside compounds.
Mae 前 (Forward)
Ma- 目 (eye) + pe 辺
Yukue 行方 (Whereabouts)
Yuku 行く (to go) + pe 辺
Uwabe 上辺 (Exterior)
Uwa- 上 (above) + pe 辺
Mizube 水辺 (Waterfront)
Mizu 水 (water) + pe 辺
The original pronunciation of 辺 was /pe/. In some words, the /p/ was dropped and in others it become voiced as [b]. Of course, as a particle, the initial consonant became dropped entirely. Even though it has been nearly 2,000 years since it first began being used as a particle, its original nominal meaning still lives on in very commonly used words.
E へ indicates movement to somewhere (far) away from where the subject currently is. For the most part, it is interchangeable with ni に. However, it must not be used to replace に for any other usage other than movement!
E へ is most associated with extravagant distances, or at least movement away from where the subject currently is, but this is not an absolute as some speakers prefer it to sound less direct/more formal. Most importantly, as a grammatical rule, e へ must never be replaced by ni に is not allowed before the particle no の.
Watashi wa О̄saka e ikimasu.
I'm going to Osaka.
Watashi wa ashita Tokushima e ikimasu.
I will go to Tokushima tomorrow.
Nuance Note: If the particle ni に were used instead of e へ in Exs. 1-2, the speaker would be implying that the stated location is their destination, whereas e へ may imply that the locale in question is in the direction of where off they are heading.
Kо̄be e fune wo mi ni ikimashita.
I went to Kobe to see the boats.
Grammar Note: The ni に in this sentence cannot be interchanged with へ as only に can follow the continuative form (連用形) of a verb.
Kanojo wa doa no tokoro e hashitte itta.
She ran to the door.
Yoku chūgoku e ikimasu ka?
Do you often go to China?
Shо̄kudo e ikimasen ka?
Why don't we go to the restaurant?
Hidari e magatte kudasai.
Please turn to the left.
8. 生徒が机の上｛に 〇・へ △｝教科書を置いた。
Seito ga tsukue no ue [ni 〇/e △] kyо̄kasho wo oita.
The student/pupil placed a textbook on top of the desk.
Sentence Note: The particle へ is unnatural because に is most appropriate when referring to movement of an object to a finite spot, especially one that isn't far away which is the case for the desk. However, some speakers will use へ in an attempt to sound more indirect/formal.
9. 学校【に ◎・へ 〇】行く途中だ。
Gakkо̄ [ni ◎/e 〇] iku tochū da.
I'm on my way to school.
Sentence Note: Some students have a long ways to get to school. If it isn't their sole destination, say they're going to a meeting and then will be doing some event elsewhere after, e へ may make more sense, but ni に is overall more likely.
10. 北朝鮮から始まる平和【への 〇・にの X】歩みを歓迎し、対話の継続を望んでおります。
Kitachо̄sen kara hajimaru heiwa [e no 〇/ni no X ] ayumi wo kangei-shi, taiwa no keizoku wo nozonde orimasu.
(We) welcome steps towards peace to be made by North Korea, and we are hoping that dialogue may continue.
Sushiya e ikimashita.
I went to a sushi restaurant.
Yoku kono izakaya e kuru n desu ka?
Yoku kono izakaya ni kuru n desu ka?
Do you often come to this pub?
Word Note: An izakaya 居酒屋 is a Japanese style pub where you can order a wide variety of foods and drinks for a low cost. They often have times or special deals for nomihо̄dai 飲み放題 (all you can drink) and tabehо̄dai 食べ放題 (all you can eat).
Particle Note: E へ always implies going off somewhere, and so it is unnatural to refer to the addressee arriving at Point A.
Kare wa ma mo naku koko e kimasu.
He will be here shortly.
Nuance Note: Ex. 13 may imply that "he" is coming from far away, and since he isn't there yet, the particle e へ can be used in conjunction with the verb kuru 来る.
Koko e suwatte hanashi wo kiite kudasai.
Come and sit down here and listen.
Grammar Note: Although originally へ should not be used to refer to arriving at Point A, in this situation, the speaker is purposely trying to be more polite by coaxing the listener over. The expectation isn't necessarily that the listener sit right next to them, which is why the sentence is not marked as ungrammatical.
Kyonen igirisu (e) ikimashita. Oranda (e) mo ikimashita.
Last year, I went to England. I also went to Holland.
Grammar Note: へ is often deleted in casual speech as is the case with the に. This is even more likely to occur when it is followed by the particle も.
Nyūyо̄ku wo tatte Shidonii e mukaimashita.
I left New York for Sydney.
Tо̄kyо̄ e shutchо̄ shimasu.
I will take a business trip to Tokyo.
Culture Note: Presenting business cards, meishi 名刺, is extremely important to business etiquette. You should present your card with both hands and take it out of a business card box, and you are to receive the other person's card, read it, and say chо̄dai-shimasu 頂戴します. When exchanging cards with someone of higher status, you should make sure yours is below the other. You should place business cards in the back of your leather case, and if you are at a table, wait until the meeting is over before putting it in. Don't write on, damage, or fold business cards, at least not in front of the person.
Nihon e kaeritai-desu.
Nihon ni modoritai-desu.
Nihon [e/ni] mata ikitai-desu.
I want to return to Japan.
Culture Note: Kaeru 帰る from a cultural standpoint refers to returning to where one belongs, a.k.a, one's home. If that is how Japan feels to you, 18a would not be incorrect, but if that perception is not there or not understood to be of that nature to the listener, a native speaker would correct you with either 18b or 18c.
Mae e susumо̄!
Let's move forward!
Mae ni susumо̄！
Let's move to the front!
Grammar Note: When specifically indicating a movement/event that is unfolding, it is unnatural to use に. As such, you will heavily encounter it in campaign-oriented language/
The combination particle e to へと is a much stronger variant that emphasizes direction. You will see this mainly in music and literature. It is almost completely interchangeable the simpler e へ except that it cannot be before the particle no の.
Heishi wa kawabe ni oritara, sugusama fuku wo nuide kawa e to tobikonde nigete itta.
When the soldier got down to the riverbank, he immediately stripped off his clothes, dove into the river, and escaped (into the distance).
Mirai e to hashire.
Run towards the future.