@Christian, Thank you for posting that link to Oxford Dictionaries It was interesting to read their description. I would still argue that both forms are correct depending on the pronunciation of the actual words together. Some people say "an hotel" without pronouncing the "h". Others say "a hotel" while pronouncing the "h". For this exercise, I think that both answers should be considered correct since it depends on how the speaker actually pronounces the word.
In Spanish you use "e" instead of "y" if the following sound is the same upsilon sound "i" (which includes words that start with "hi" since "h" is silent IN SPANISH) to avoid repeating the same sound which can be awkward to say and sound awkward if not blurred together.
In English, "h" is not silent (except in some dialects which are exceptions to the rule", it is a pronounced consonant. "A" is used before words that begin with consonant sounds. "An" is used before words that begin with vowel sounds.
This is also to avoid awkward English pronunciation and sound. Whenever possible Anglophones avoid pronouncing the hated glottal stop, for example in "a apple" or "an car", which are annoying to say with the glottal stop in the throat, interrupt the flow of speech, and sound strange to native English ear, and are consequently grammatically incorrect since English adopted the ancient Greek "moveable nu" rule: "a" becoming "an" before vowels.
In some dialect where "h" is not pronounced, "an hotel" may be colloquially fine, but "a hotel" is the proper standard form.
Just like "a house", "a home", "a husband", "a harvest", "a harp". These would all sound and be incorrect with "an" in standard English where consonant "h" is pronounced at the start of the words.
on the question of an or a I personally would never use an hotel. my though is I go in this instance is not how anything. it is at the least curt, I will go to a hotel, I will stay at a hotel. I go to, is a translation not manner in which we communicate. americans that is.