How can I search items based on their location?

The search calls in the Finding API allow you to perform proximity searches.

Supply a postal code in the buyerPostalCode field and specify the maximum distance to search for items in the item filter MaxDistance field. eBay returns only those items that are found within the specified distance from the supplied postal code. The distance will be calculated in the units that are local to the specified postal code (kilometers or miles).This type of search is called a "proximity" search.

Here is a sample -