I'm setting up a business directory for Bangkok with hotels based on the BizReview theme/installation profile.

SETUP
Content type
In order to store bussiness locations I use a content type with a field using a Geofield field type provided by the Geofield module with a Google map widget provided by the Geofield Gmap module.
Map
On my homepage I have a Leaflet map view with Format set to Map (Leaflet API, via IPGV&M) (provided by the IP Geolocation Views & Maps module) listing all the businesses added with the business content type.

MY NEED
I would like to add an auto-complete search box to search the map on my homepage, like the one on google maps. I tried to find a module for this but couldn't find one. I only found modules that add a field to a content type (e.g. Google Places for Drupal). The Geofield Gmap module basically does what I need but on a content type instead of a map. If I add a business I can use the ''Geocode address'' field to lookup a location and the location gets displayed in a map (see image on the module page).

SOLUTIONS?
1. Is it possible to reuse the search field provided by the Geofield Gmap module on the map on my front page so that visitors can search for a place in Bangkok and see all the hotels that I added that are nearby? Maybe with views or a hook & custom field template.
2. Is there a module for this (I searched but couldn't find one)?
3. Can I use Google Places API and a Places search box and add the html for the search box and the classes to the html of my map. Or would this require more modifications (my knowledge of PHP is limited but good enough to implement hooks and make a template).

Any help would be much appreciated.
Jasper