score:9
Everyone's favourite Mapping, Public Transport and Governance geeks MySociety did some some work on this very question a few years ago. As part of this, they handily produced maps showing travel time by public transport from both Cambridge:
And from Oxford:
For a weekend away, you probably want to restrict yourself to regions that are at the red end of the spectrum, so you have enough time to enjoy where you're going!
Sadly, producing these maps isn't a 1 minute job, so they're not just available for everywhere. For maps from other starting locations, or for a given ending location, you need to order your custom map from their shop, which are Β£25 for one. Money raised from it goes to support their other charitable work. As it requires people to manually generate and tweak the map, I'm told it normally takes a day but might be a bit longer if they're all busy...!