Geocoder

You can use the default ArcGIS [Class:Geocoder] (https://developers.arcgis.com/javascript/jsapi/geocoder-amd.html) or a custom geocoder

Example Config Object for default Geocoder

geocoder: {
    include: true,
    id: 'geocoder',
    type: 'domNode',
    path: 'esri/dijit/Geocoder',
    srcNodeRef: 'geocodeDijit',
    options: {
        map: true,
        mapRightClickMenu: true,
        geocoderOptions: {
          autoComplete: true,
          arcgisGeocoder: {
             placeholder: 'Enter an address or place'
          }
        }
    }
},

If the width of the search box for the geocoder widget is not wide enough you can alter viewer\js\gis\dijit\Geocoder\css\Geocoder.css

Try using (or altering) both of the width values below that will work for your implementation

.gis_GeocoderDijit .searchContainer {
    position: absolute;
    top: 0;
    left: 100%;
    width: 250px;
}
.gis_GeocoderDijit .esriGeocoderResults {
    display: none;
    z-index: 99;
    width: 279px;
    position: absolute;
    left: 0;
    top: 100%;
    margin: -3px 0 0 -31px;
    border: 1px solid #57585A;
    border-top: 0;
    padding: 0;
    background: #fff;
    -webkit-border-radius: 0 0 5px 5px;
    border-radius: 0 0 5px 5px;
}

Example Config Object for custom Geocoder

geocoder: {
    include: true,
    id: 'geocoder',
    type: 'domNode',
    path: 'gis/dijit/Geocoder',
    srcNodeRef: 'geocodeDijit',
    options: {
        map: true,
        mapRightClickMenu: true,
        geocoderOptions: {
            autoComplete: true,
            arcgisGeocoder: true, //if true a pick list showing your custom geocoder(s) below and the ESRI widget will appear for the end user to select
                zoomScale: 1000,
                placeholder: 'Search for an address',
                // name below will appear in widget pick list if arcgisGeocoder:true
                geocoders: [{ url: 'http://ServerName/arcgis/rest/services/GeocodeServiceName/GeocodeServer',
                      name: 'My Address Points'
               }]
        }
    }
},