Hi Cesar. Thanks for your questions.
The “Near” field that Pro adds to the Tribe Bar is from this file: /wp-content/plugins/events-calendar-pro/src/Tribe/Geo_Loc.php
The default geofence radius is 25 miles, which can be filtered — find function get_geofence_size() in that file.
As far as autofilling the search field, you can just link to your site’s search — like this being the URL for searching “New York, NY, USA”: yoursite/events/2016-02/?tribe-bar-geoloc-lat=40.7127837&tribe-bar-geoloc-lng=-74.00594130000002&tribe-bar-geoloc=New+York%2C+NY%2C+USA — just remove the “2016-02/” part so it doesn’t always go to February 2016.
If you prefer a shorter URL: yoursite/events/?tribe-bar-geoloc=New+York%2C+NY%2C+USA will autofill the field but not actually filter the results. In other words, they’d still need to click the “Find Events” button to submit the search.
I hope this is the information you were looking for.