The map object has several methods for displaying a particular view, be it centring on a MapPoint or other geometry. For example, you could use Map.centerAt(mapPoint) if you had a map point. What you want to do is centre on the extent of the tiled map service you've loaded so you can use map.setExtent(extent, fit) passing it the extent of the tiled service and the Boolean fit if you want it to zoom as required to fit the whole extent. You can get the extent of the tiled service using TiledMapServiceLayer.fullExtent property. For example:
map.setExtent(tiled.fullExtent, true);
You can subsequently put this into your check box event function so that every time it's checked it zooms to the extent (if that's how you want it to behave, another option might be to have the checkbox click event just toggle the layers visibility but then have a 'goto' button next to it that zooms to it).
You can check out more documentiontation for the map object and all of the ArcGIS API here: https://developers.arcgis.com/javascript/jsapi/map-amd.html
Hope this helps.
Edit: As per your comment, trying to access the fullExtent property straight after the call to load the layer doesn't work because addLayer is asynchronous and so execution returns before the layer is loaded. To set the extent straight as soon as the layer is loaded, you need to register a function to run when the layers onLoad event is raised. The following code should achieve this:
var tiled = new Tiled("http://xx.xxx.xx.xx:xxxx/arcgis/rest/services/USA/NewYork_tiles/MapServer");
tiled.on("load", displayLayerExtent);
map.addLayer(tiled);
function displayLayerExtent(evt) {
map.setExtent(evt.layer.fullExtent, true);
}