For some parts of the world "an hotel" is correct and this is exactly what I used when I lived in Canada and how I was taught. Language is always evolving. But, I am now going to quote what someone on StackExchange said: "Queen Elizabeth II is one such person who could correctly say (an) historic event". "President Obama is one such person who could correctly say (a) historic event". If the H is silent, it is pronounced: an otel and an istoric event like the Queen would say. If the h is not silent, it is pronounced a hotel and a historic event like President Obama would say.
You only use "an" in front of a word that begins with 'h' if that 'h' is silent.
- an hour, an honourable mention
- a house, a human, a ham sandwich, a hopeful sigh
The words "hotel", "horrific", and "historic" (which are often the disputed ones) are nowadays usually pronounced with an initial 'h', so using "an" with them is usually pointless.
'The words "hotel", "horrific", and "historic" are nowadays usually pronounced with an initial 'h'. Sorry I disagree; you mostly hear them in the UK without the 'h'. For example:-an (h)orrific event, an (h)istoric building, I bought an (h)otel. This is how I was taught to speak, initially by my mother, then at secondary and grammar school. Just because young people nowadays have no language skills, preferring to text rather than actually speak to anyone, doesn't mean the lessons we learnt back when English was taught properly have been completely forgotten. Sadly it seems they eventually will be but I won't be around then, thank goodness.
Proper English is whatever the majority agree on is proper. And not pronouncing the 'h' in those words is falling out of use. Older people still tend to do it, but the language is shifting, like always. It might be common in your corner of the country, but the Oxford University, whose article I linked, is UK-based as well, and only records the pronounciations with initial 'h'.
"beside the hotel" is wrong, but "next to the hotel" is correct? Que lastima!