So, several points about this
1) Cheap = дешевий, inexpensive = недорогий
2) The word дешевий has the same negative connotation as "cheap" has in English.
3) Cheap ≠ inexpensive. Something can be inexpensive, but not cheap. Not only because of the connotation, simply because not being expensive, or being affordable, doesn't mean being cheap. E.g. 30€/night for an AirBnB is inexpensive but not cheap (my example can be subjective)
We should either accept inexpensive as a translation for дешевий and недорогий as a translation for "cheap", or not accept. Right now in most of the exercises this is not accepted, in some it is. For example, here it is because @SergioRuido responded to your comment. But he didn't go through all the exercises containing the word "дешевий" adding it there too.
So, with all these points I would rather remove "inexpensive" than add it where it's missing. If you have another opinion please tell me, it's not so hard to add it, if I change my mind I can :)
If that's the case, it's pretty weird to pointedly go in search of a cheesy hotel unless, perhaps, you're a pimp, a mobster or a film producer in need of a seedy dive for a sleazy encounter.
If, on the other hand, you're a tourist looking for affordable accommodations, it makes a lot more sense to ask about an inexpensive hotel.
I don't have a problem learning the Ukrainian word for cheap, but it would be more appropriate in a useful context: The actor wears cheap jewellery. The kiosk sells cheap souvenirs. The hotel is cheap, but it's noisy and has bedbugs.