The code you have creates a new SharePoint site as a subsite of the current website. The URL for the subsite is {parent site URL}/{subsite URL}. So, using the code you have above, the URL for the subsite will be https://xxxxxxxxxx.sharepoint.com/MyShineyNewSite. This URL structure is inherent to SharePoint and cannot be changed.
You can use different code to create a new SharePoint site as the root of a new site collection. By default, the URL of the root site of a site collection is {tenant root site URL}/sites/{site collection root site URL}. In your case that could be https://xxxxxxxxxx.sharepoint.com/sites/MyShineyNewSite. Again, this URL structure is inherent to SharePoint and cannot be changed.
This blog post covers how to create a site collection in SharePoint Online using the Client Object Model: