What computer information can WiFi networks see?

This started off as a comment on Snappie's answer, but it's getting a bit long...

Assume all data is encrypted using SSL

But not all data is encrypted!

(in addition to IP address, and the amount of data being passed in either direction...)

They can also see the IP names of all the resources you access (including web) from your DNS activity (not encrypted). If you are using a proxy, then this is also exposed in the proxy logs.

They can see what type of network interface you have (from the MAC address).

They can see when your computer connects to the network (Wifi connect, DHCP).

From passive sniffing of encrypted traffic they could probably guess what family of OS you are using.

I believe Chrome can be quite chatty as it tries to work out if something is a URL or a search term and tries to diagnose what network connectivity it has. I would presume that this could be exploited to determine if you are using Chrome, although its not something I know a great deal about.

If, at any time, your browser does make a non-encrypted request, then this will reveal a lot of details about your browser and OS. Depending on the service, it may also reveal a lot about your affiliation to the site.

...and this is just from passive data collection. If they choose to start sending data at your device, it will reveal a lot more.

They may see the names, IP addresses, and possibly MAC addresses of other computers on your home network that you may communicate with, often this will be wireless printers, but may include gaming consoles or smart televisions that you have connected to in the past.

The MAC addresses your computer asks to resolve are interesting. MAC addresses are assigned to manufacturers, and are baked into the chips of every network adapter. The address can reveal the chipmaker and/or the device manufacturer, and require a certain level of technical competence to change or forge. They can provide corroborating evidence that two computers that are making ARP requests for the same MAC addresses may have a shared external connection: e.g. if both your PC and another PC are requesting resolution of the same MAC addresses belonging to a wireless printer, an investigator may assume they share the same home network, therefore their owners may have a relationship.

They will see the "community names" of any SNMP devices you may manage, such as routers or switches. Because SNMP is not a secure protocol, the community name itself serves as a de facto password (although the chances are high that it's set to the default value of "public" anyway.)

If you have a mail client that isn't properly configured to use TLS, they will be able to read your email.

Every auto-updating program you have "phones home" to check for new versions (Windows, iTunes, Firefox, Adobe, Java, cloud providers like dropbox, etc.) Some have little auto-updater tasks living in the taskbar, which send requests even when you're not running the program in question. These requests reveal some of the programs you have installed.

In addition to the information you already named:

• They can see the IP address of the websites you are visiting. This is not encrypted. Thus they can figure out what websites you are visiting. I think this is what your school is probably most interested in.
• The size of the requests and the size responses from and to the websites you visit. Even if it's encrypted the size of the package can give information about what you are doing.