Among all the exported data, some can be redundant with regards to the local configuration. So it is possible to choose the priority to be allocated to every source (local, NIS or other). To do so, you can use the Client Services button on each NIS client. It allows to choose the preferred order to search for data. For example, you can choose to resolve the host's addresses using 1) the file /etc/hosts, 2) then the NIS hosts served (if you selected it in the NIS table), 3) and finally (if the client cannot resolve any more), use the DNS server.
To verify that the client communicates with the server, you can use the ypcat passwd command to read the password data served by the server.
If you export your user's directories (using NFS for example), and if you start the autofs service on your NIS client, users should be able to automatically mount their own home directory when they log onto the client. This way, everybody can automatically log on every client, having all their personal data and configuration files.