More info.
Bonjour items (other computers) are supposed to show in the Finder's Side bar under Shares as has been said.
Most routers would allow local traffic (Data to flow around your LAN).
To show up in the Side Bar as a share port 5353 on the UDP Protocol should be open.
The Account in iChat or Messages also uses this (it is the discovery port as it were)
The Account goes on to use port 5297 and 5298 (both on UDP and the 5298 also on TCP).
This info comes from here Using iChat with a firewall or NAT router - Apple Support
See Note 2 at the bottom in particular.
Do either of you have additional software like Little Snitch that acts like a firewall in certain actions ?
This also might help. http://blog.spikie.info/osx-10-10-yosemite-how-to-disable-bonjour-service-advert ising-without-disabling-dns/
The Advertising of Bonjour can be turned Off. (it is mDNS and is linked to everyday DNS).
The link explains it used to be listed as Multicast and is now a Discoveryd item in
LaunchDaemons
The article lists the old Knowledge Doc item (Apple Instruction here:http://support.apple.com/kb/ht3789) that are not longer there.
However it might be it was "disabled" under an earlier OS version and has not been updated to be On again.

9:20 p.m. Friday; August 7, 2015
iMac 2.5Ghz i5 2011 (Mavericks 10.9)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad