Since I started my library career several years ago, and particularly since I've been living in London, I've been on many different library visits. However, few if any of them have related to my current job as an Information Officer working with a VLE. Places I've visited over the years have included the Wallace Collection, RADA, St Paul's Cathedral, the British Library, Conway Hall, ZSL London and Shakespeare's Globe.
In fairness I'm not sure there would be any point in a visit focusing on an institution's VLE. I don't think sitting in front of a computer would make for a particularly fascinating day out, and I feel I can learn about this sort of thing from user groups, conferences and online discussions. I don't feel that I learn anything particularly related to my everyday work from these visits.
My job is focused on technology and e-learning, and that's something I enjoy and find interesting. But I have a strong interest in special libraries, involving rare collections or history or heritage, and these visits allow me to explore that. Furthermore I have visited a school library and some academic libraries, which also allow me to experience the breadth of library services and the variety of roles that are available. Library visits help me to feel part of a profession; they help reinforce there is a whole world of libraries out there and help me to see the bigger picture.
My ultimate conclusion is that, even though there is no immediate practical benefit to my visits, I get other things out of them instead. So for me they are definitely worth it.