If anyone else should need the solution I found, here it is.
Using WAMP (Uniserver)
Using sub-directories not sub-domains
Changing to a different theme and seeing that the links worked narrowed it down to the theme being the problem.
The first blog at '/' was listed in the options table as /blog/path
Changing it to /path made the links for the Categories, Archives, and Recent Posts link to work.
All my other settings looked ok.
Now it works.
I hope I can save someone else some time with this