When used with something like hotel, "cheap" usually has a connotation of low quality, as well as price. Consequently, I would ptobably say that I was looking for an "inexpensive" hotel.
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 :)
Sorry to have put this note in the comments, since I realize that is not the place to suggest an addition, but I thought this subtlety might be interesting to those also learning English.
I would say that "дешевий" implies low quality in Ukrainian as well. To avoid that connotation, one can say "недорогий".
ya shukayu can not also mean I am searching..?