As long as it is the local network and as long as the router (or other network infrastructure) does not disallow it you can use a UDP. When a server comes on line and perhaps and timed intervals after that it broadcasts a "Server here" message on a UDP port.
Clients listen on the UDP port and collect addresses.
The alternative to that, when UDP is not possible (internet) is to have a dedicated communications server that is accessible to everyone. It does nothing but indicate what servers are up. Servers post availability and clients request server lists.
Thank you for the response. After checking my router and looking around a bit, I see the UDP block operations are disabled on my router, so I do not think I will be persuing that avenue, and realistically this is going to be me and my family and maybe a few friends sitting around the house with our laptops and somebody says: Hey, let's play XYZ game so the lookup server options is not a good scenario either.
It did give me a reality check though -- I realistically can expect to only have to check the first few local IP addresses for this type of implementation, so the bruit force approach will work ok on the scale I'm implementing.
Thank you for your input!