"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.
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.