In 2013, in a bid to combat Vaccine Hesitancy (VH) and provide information on vaccines by communicating with the general public and the health community (e.g., healthcare workers and public health operators), the Italian Society of Hygiene and Preventive Medicine (S.It.I.) published the national website “VaccinarSì”. The project was subsequently extended to ten Italian Regions. This led to the creation of the VaccinarSì Network, whose websites are publicly owned. The aim of this work was to present the framework of the websites of the VaccinarSì Network and to analyse user behaviour in the pre-COVID-19-era (dating from each website’s publication until 31 January 2020) and in the COVID-19-era (from 1 February 2020 to 31 January 2021). Some metrics such as the number of visits to the site (sessions, number of users and average session duration), user behaviour (pages viewed, bounce rate and organic search) and the session acquisition path (direct traffic, referrals and social traffic) were searched, extrapolated and processed with Google Analytics. Qualitative and normally distributed quantitative variables were summarised with their absolute (relative) frequencies and means. Statistical differences between the means of the two periods were evaluated through paired t-test. A two-tailed p-value less than 0.05 was considered to be statistically significant. When the total values recorded over the period were compared, an overall increase in metrics was observed—the number of individual users, visits and individual pageviews rose in a statistically significant way. Our study aimed to highlight how combining disciplines such as health education and digital communication via Information and Communication Technologies (ICT) represents the best strategy to support citizens. This approach gives them the tools to become independent and responsible players that are capable of voluntarily and consciously choosing to adhere to vaccination programs. The VaccinarSì Network’s goal for the future is to reach an even wider audience. By building each user’s critical knowledge, this network enables users to be active components of a wider, more empowered community.