Since this is the top result on Google for “Discourse list unanswered topics”, and the discussion is too technical for some, the bottom line is:
You can see a nice list of unanswered topics by using a URL like this (which you can bookmark in your browser if you use it often).
https://discourse.example.com/latest?max_posts=1
For me, this would fit perfectly right there on the top, alongside Unread and Top links. I assume this is a very typical use case, at least for moderators.