ほぼ全ての日本のホテルでインターネットが利用できます。って英語でなんて言うの？

1. Most hotels in Japan have wifi access.
   Internet connection that is available at hotels is commonly known as wifi connection. You can also use the word "most" which is another way of saying "almost".

   Hope this helps.

"Internet access is an amenity in most Japanese hotels," is the most thorough way to say this. Amenity is a word that refers to a useful feature of a building. Some amenities are free, others are available, but you must pay for them. Most is a way to say almost all.
"Almost all hotels in Japan have internet access available," shows that in most hotels you would visit in Japan, you could access internet if you wish.
"There is free wifi in almost all Japanese hotels," is the most common way that we would state this. Wifi means anything that allows devices to communicate wirelessly, but usually we think about wireless internet being available when we hear this term. Most commonly, this is a free service, but at times there is a charge. In this case, I stated that there is a free wifi, meaning there is no charge to access the wireless internet.

To be able to use something is also called 'access' so to be able to use the internet is called 'internet access' this can also be called 'wifi'
If you are talking about most of something then you can say 'nearly all' or 'almost all'

Most hotels in Japan have free wifi. - this just tells people that the wifi at hotels in Japan are free.
Most hotels in Japan supply easy internet access. - this response informs your audience that internet access at hotels in Japan are available in most places.

An amenity is a feature of a hotel room. Other amenities would include a minibar in the room or a concierge service.

Something is ubiquitous if it is available anywhere. Coca-cola, for example, is ubiquitous. You can find it just about anywhere.