Looking for wp plugin, theme or search term - Filter & Search

hello together,

for my future wordpress travel blog/portal I'm looking for a possibility to realize a filter form how U can see on the left side of the image. the user should have the option filtering for example destination, area, hotel or apartment, equipment, rooms, dogs allowed or not and the system delivers the results of the search options. is somebody here who know a suitable wp theme to manage it. or a plugin with this functions? which detailed keyword I have to use if I want to search in GOO LE? what would you fill in the search mask finding a solution for my question? a short helping advise would be really great. thanks in advanced...

Are these the kind of plugins you are looking for?