Checking links of your website is an ongoing process and this way you can identify and rectify your broken links immediately and keep your website alive. Both internal and external links have to be checked. Any broken links can be fixed immediately.
You analytics data can be a base on which you can decide where you should be starting. It can be cleaning up the content or going for new ventures. Web analytics gives a lot of information about the visitors like how they landed on this page, where would they go next, how they would exit from the current page and what type of device is being used by them to view your website.
Such information can help you decide on what kind of venture should you go next. For example, if your website is frequented on mobile phones, you can think of making it more mobile friendly. Cleaning up unwanted content or giving more information on particular pages to make the visitor stay longer at that page and other changes can be made on the basis of information obtained from analytics data.