>I love to sit with a mouse in one hand and a coffee in the other

In my opinion, the best place to have a mouse in one hand and a coffee in the other is Cafe Rouge in Little Clarendon Street.

You might want to try some of the locations listed at: http://www.oxfordcityguide.com/WiFi.html.

Whether or not you need to sign on is another question. Bear in mind that many commercial places offering this service need to get people to log on via their provider in order to be able to "indemnify" themselves against misuse of their service (criminal behaviour being a big one). Businesses open themselves up to misuse if they do not insist on logging in.

There's now a second Greens Cafat the end of Queen St (opposite the Westgate) with free open wifi. Also G&D's on the Cowley Road.

The Open Guide to Oxford has a category specifically for Free Wifi (though it may not be current): http://preview.tinyurl.com/oxfordfreewifi

You could try Daily Info's Wifi Hotspot page which lists the providers:
http://www.dailyinfo.co.uk/whatson/wifi.htm
and there's also this interactive Google map:
http://www.wifi-in-oxford.co.uk/