Registration is a one time thing.
Now if you are staying in a hotel with a tourist visa, the hotel, when they are officiallly allowed to do that, will register for you. If you are staying in an apartment on a private visa, you will have to register yourself. The amount of money is negligable in this case. Personally I can stay, because of my work only one week per month in Ukraine, so therefore I do it via my guide. Check the board for opinions about him.