Searching for academic jobs within a specific city
If you intend to stay on the job market (whether for those 3 institutions or in general), the best thing you can do is stay competitive in terms of research productivity. That usually means taking a postdoc or other full-time research position where you can publish as much as possible.
However, there is a &quot;shelf life&quot; to postdocs. If you are a postdoc for too long, hiring committees start to wonder why you haven't been hired, and may reject you thinking there's something wrong. For instance, in my field it is common to have 0-2 years of postdoc, so someone who has been a postdoc for 5 years may find it more difficult to get interviews.