Hi there - first of all, welcome to the EE community!
Yes, there is search functionality from EE natively. The details, including some examples, can be found in the documentation.
Based on your example, though, the search module may not be the most appropriate way to go. Since your search is intended to be largely geographically based, one of the more robust search tools you might choose to use would be tapping into the Google mapping API so you can perform true geographic searches (as opposed to simple matching of country or town, for example). There are several Google Map add-ons that do all the “tapping in” for you, creating a field type for you to generate the map and conduct geo-located searches. If you visit devot-ee.com (the main add-on collection for the EE community), and search for “Google Map”, you’ll find several options. I’m personally a big fan of the one from ObjectiveHTML called “Google Maps for ExpressionEngine”.
However you decide to proceed, you shouldn’t have too much trouble implementing a search. I only suggest an add-on because of the geographic nature of the search you’re aiming for. That approach would actually add additional functionality for your user by allowing you to tap into Google’s mapping features, like directions, street view, etc.
Cheers,
John