Your ngClick is correct; you just need the right service. $location is what you're looking for. Check out the docs for the full details, but the solution to your specific question is this:
$location.path( '/new-page.html' );
The $location service will add the hash (#) if it's appropriate based on your current settings and ensure no page reload occurs.
You could also do something more flexible with a directive if you so chose:
.directive( 'goClick', function ( $location ) {
return function ( scope, element, attrs ) {
var path;
attrs.$observe( 'goClick', function (val) {
path = val;
});
element.bind( 'click', function () {
scope.$apply( function () {
$location.path( path );
});
});
};
});
And then you could use it on anything:
<button go-click="/go/to/this">Click!</button>
There are many ways to improve this directive; it's merely to show what could be done. Here's a Plunker demonstrating it in action: http://plnkr.co/edit/870E3psx7NhsvJ4mNcd2?p=preview.