Your printer provides a file share for dropping files into or are you just trying to locate the printer on your network?
Does your new multifunction printer support Bonjour/ZeroConf? (Most new network based printers do) If so you can use a program such as Bonjour Browser to see what is available on your network.
On your router does it appear on the DHCP Clients Table (you may have to consult your manual to see how to see this table) - as this will also give you the IP but will also let you know for certain that your printer is actually connected to your network.
From your Mac itself you can use a program such as Nmap from the command line or use a GUI based app (eg. Zenmap - GUI for Nmap or AngryIPScanner) to scan your network and then see what ports are available.