I will encourage faculty's presence on academic web2 environments like ResearchGate etc. Since users of these platforms include their affiliations, they are more likely to redirect readers of their publications to the university's website.
Again, it is also a fact that institutions who have functional Institutional Repositories have increase traffic on their university websites.
In ranking universities by Web metrics it is important to normalize indicators. There are universities that are younger than others, and those that serve less population than others, and those that are affiliated less than others with medical schools, etc'.
Definitely good researches with high impact will increase your university impact, in addition to that your university should be helpful and active in your society.