Tor traffic over a local network will look exactly like what it looks like on the outside. There is no URL/DNS info leaked.
You can verify that by yourself by running a packet sniffer on your computer. I recommend WireShark which is available for Windows, Mac OS X and Linux.
Open WireShark, select the network interface you want to sniff on (Ethernet or Wireless or etc), and then press the green Start button, and it will show you all packets that pass by (in or out) your network card in real time.
You can filter the results by writing http or dns in the 'filter' field, or from the menu Capture -> Capture filters. Be aware that if you want to change the filter, you may have to stop the capturing and restart it.