There is no singular site to get general "application suggestions".
People recommend software and web applications to solve programming problems on Stack Overflow all the time, without the question migrated to Super User or the web applications location for the answer. This is because the solution is not the question.
Think about what site is most appropriate for the task you are trying to accomplish. Most of IT tends to fit within the trilogy - you ask on Stack Overflow if you're looking for an application regarding your coding, Server Fault if you're looking for an application for server management or networking, or on Super User if your task is concerning software or software management. Don't necessarily ask for an application specifically - focus more on what the problem you need to solve is, and what you've tried if there's been that. Application-based answers will come naturally where they are most applicable.
I'd start from the trilogy, and move to the satellite sites when it's appropriate (like if you specifically need a web application, you can head to the corresponding area). Of course, always evaluate the FAQ for the site before you ask on a new site.