How to fix hotel WiFi?

The thing in the wall is a phone jack.

For hotels, repeaters are a bad idea as every time you go through one, you cut the speed in half.

Hotels need to use Mesh networks. No idea if you can do that without owner cooperation.

Mesh networks receive data on a different channel than they send it on so they don't cut the speed in half. Most are also self adjusting meaning they do things to maximize the speed.

You're going to have to purchase routers that are Linux programmable to be repeaters the best thing to do is to goes to a computer network store and tell the band that you live at a motel complex and want to extend the range of the Wi-Fi signal from the ethernet cord all through the building take back the things that you have already bought their totally worthless they're not going to work when you get the router use the same exact username and password that's on the main router that way all you have to do is to plug them in throughout the building if you get good rotors that are properly programmed you will have no problem you may also just want to call the computer store and have the network specialist come and fix the problem you're going to spend more time trying to buy cheap plastic garbage repeaters from the store that do not work then if you actually go buy a set of Linksys programmable routers

Is it your hotel, or are you just a resident?

If it is your own hotel, forget about WiFi repeaters and install wireless access point connected either directly by Ethernet or using Powerline network adapters back to the router.

If you are a resident then, if you can get permission from the hotel owners, install a Powerline network connection from the router to your room.

Since Ethernet connectors are generally a standard size pretty much world wide, then I suspect that you do not have the proper cables.

Finally, although chaining WiFi repeaters can be made to work, since each repeater is a store THEN forward device, you should anticipate a 50% drop going through each repeater. (They cannot receive signal and transmit at the same time, hence store THEN forward.) A chain of n such repeaters can drop the speed by a factor of 2^n. so (say) a chain of 3 repeaters might yield only one eighth of the speed.

I hope this helps.

How is the Ethernet cable small ?