Setting up a local web server would be a good way to test your site's performance, although you'd mostly be ruling out whether or not dedicated resources and unlimited bandwidth were the issue in that case. You may also benefit from troubleshooting load times for simpler content on your website, such as plain html web pages with no client scripts or server-side programming within them needing to be executed, or images and videos of various file sizes to determine if it's a bandwidth, request handling, or code performance issue.