"Better" would be used for the quality of the hotel, whereas 'nicer' would only be used for the appearance of the place.
It is a better hotel - This means that the service and staff are very good and friendly and maybe even the beds are cosy
It is a nicer hotel - This means that the appearance of the building (and inside, too) is more appealing
Remember that 'better' is the comparative of 'good'. 'Good' is used to describe quality and 'nice' to describe appearance.
Why not "finer"? It's closer to the meaning you attribute to "better" and this should be a good enough explanation, but maybe this something a native could help with. Is the adjective "fin" really used in such a narrow way or its meaning could actually be broader?
I might be sleep deprived, but I thought that "det här" was "that" and "den här" was "this." I have tried using the idea that det ends in t same as that to remember, am I mistaken?
här is 'here' and där is 'there'. den här and det här are 'this', den där and det där are 'that'.
I think I have come up with a new, better mnemonic device
"den-det här" is effectively "this here"
"den-det där" is effectively "that there"
Both implicitly minus the here-there. Basically, you could say "this here object" or "that there object" but you could never say "this there object" or "that here object." It works for me, I hope it works for other native English speakers as well.
This is how I remember this construction..."this here" and "that there" are common in informal English, especially in the American South.
Ah, I was looking at the wrong word. Well scrap that mnemonic device. Tack!
''Finare'' can also mean prettier. Duolingo, I think you should ad that as a potential answer.