Applicationn using Socket & ServerSocket Classes whereby clients automatically discover LAN Server

I've got an application that I'd like to have triggered / controlled over a LAN (always a private LAN and same network) that regardless of the DHCP details, clients discover the server and are able to communicate automatically without having to input relative IP's. 

To add a wrinkle, there will be multiple client Socket objects on the network that need to discover the ServerSocket automatically. 

I'm unsure if the classes I've chosen are appropriate for what I'm trying to do.  The Server will be passing keyCodes to the various clients simultaneously.  I thought it would make sense to have each remote node be a client instead of a server in this case?

Thanks in advance for any advice you can lend!