The space constraints can be solved. The filters can be neatly arranged under the search bar, in dropdowns, with some indication of activity state when not expanded. Any active filter can appear as a tag label in the search bar (with a click or to dismiss or backspace at the start of the search bar to pop).

An excellent search bar might offer filter-suggestions as you type into the search bar, e.g. typing “Richmond” might show you a neighborhood filter for “The Richmond”, a city filter for “Richmond” along with the general search term “Richmond”.

This way the filter only occupy some cheap vertical space which can be scrolled passed, with only active filters taking some space horizontal from the search bar (which can always just wrap anyway).