Hey @callen.hedglen! 
There isn’t currently a way to add filters to the searchbox element when searching for Geographic Places. However, Bubble’s searchbox element uses the Google Places API, and you can use an input element and a repeating group underneath to achieve a similar UI:
To set this up, you can install the Bubble’s Google Places API plugin and obtain a Google Places API key from Google. I’m not 100% sure how you would only display Cities, but to start, I think the type of Google Places search would be a Nearby Search:
The searchbox on the page below would contain the State where the User lives, and the repeating group would automatically display Google Places within X miles (radius) of the Searchbox location.
Preview:
Editor: