So he definitely doesn't need a master server
I wouldn't rule out the master server solution so fast imho ^^.
First, it's unclear what his needs are ; whilst I agree he stated it's for LAN use at the moment, the broadcast solution has a severe pitfall in that it limits the number of server instances to one per computer. To get rid of that limitation, you can either broadcast to multiple ports (but you're still limited to the number of broadcast messages you send), or you can use an external source to gather infos about ongoing servers.
Secondly, the master server solution scales better (internet, lots of server on LAN, etc...) and is a "cleaner" solution imho
.
To sum it up :
broadcast => easy and fast to implement (but some limitations).
master server => more code / logic to implement, but cleaner imho^^.
Cheers