For the wired connections, if there is a discovery protocol running, then you can typically find out to which switch you are connected, which port in the switch, which VLAN, and other information. Don't be surprised if this isn't running on a port to which you connect, as it is generally a best practice to have this turned off.
There are multiple discovery protocols, standards based or proprietary, but it is most common to find one of two. The first is CDP or Cisco Discovery Protocol, which as the name implies is something run by Cisco devices. The second is LLDP or Link Layer Discovery Protocol, which is a IEEE standard for exchanging this information.
You can use tcpdump in any *nix based OS (you may need to install, but generally it already will be) to view this information with the following commands (substituting the appropriate interface).
For CDP:
tcpdump -nn -v -i eth0 -s 1500 -c 1 'ether[20:2] == 0x2000'
For LLDP:
tcpdump -nn -v -i eth0 -s 1500 -c 1 'ether proto 0x88cc'
You can also use Wireshark or any other packet capture tool if you prefer (display filters in Wireshark are just "cdp" or "lldp"). Additionally, there are software packages that are written to listen for this information, but I am not familiar with them myself (I generally stick to captures).