Help to create Depended Dropdown Lists Search! Just look!

Hello everybody! Please-please, Help implement next thing on Drupal 7. Now I try to explain what I need. Already spent 4 days trying to make just this thing and without success. Any help will be appreciated.
I guess everybody met such a thing as ‘Country and City’ Search. It are usually depended lists. Two dropdown lists. It think it is clear what it is. You could meet something like this on any site with hotels, hostels, plain tickets booking etc. So, I want to do the same.
I’m using Search API module and its extensions to realize it.
I need somehow to implement instead of the usual search text area input the taxonomy hierarchy dropdown lists. I have taxonomy with double hierarchy. Maybe I don’t need to use the taxonomy. Maybe there is another way to do this. Let me know, please!
Actually I can realize it as one dropdown list with help of views or Search Page module (Search API extensions).
In this case it looks like:
USA
- New-York
- AL
- …
Canada
- Ontario
- …
It is one dropdown list with all term translations in it. (I need just one current user language).
But I need two. There is no widget to make it as two dropdown windows.
Simple Hierarchical Select and Hierarchical Select widgets are good for me, but it don’t appear in (index) view just in (content) view.
I need to use Search API, Sort and Facets. That’s why I can’t use (content) view.
Maybe, there is still a widget which I can use.
Or I can realize this in other way. Maybe, taxonomy is not necessary.
I’m not familiar in php programing, but I can try if it is easy.
So, THANK YOU FOR ANY HELP AND ANSWER!