Rather than just sharing files, it would be great to be able to push them, too.

A user running gnome-user-share on a LAN should be able to receive files via a push action, too. It would work like this:

In addition to "Share Files over the network" there would be an option to "Receive Files over the network" (mirroring the bluetooth options). When enabled, a push request would come in, a transfer would start, and put the file in Downloads.

On the other side of things (the remote computer), there would be a new option in the "Send to..." dialog's "Send as:" option for "Nearby Computer (zeroconf)". When selected, the "Send to:" list would be populated with LAN machines, with designations including the username and hostname ("burner@phoenix.local"). Once the destination is selected, pressing "Send" would initiate the transfer.

I don't know if there's a data push spec for zeroconf, but if not, the mechanics of file transfer could be done using any number of low level protocols (HTTP PUT, FTP, or whatever).