How can I work out where I can go for a weekend away by public transport, starting from Oxford or Cambridge

To help out some friends, I'm trying to work out where you can get to for a weekend away, starting in either Oxford or Cambridge, travelling only by public transport.

Are there any tools / websites / maps / books / etc that I could use to work out where I can get to in a sensible amount of time by public transport, from starting in those two cities? I would like to be able to work out the regions that can be reached in a sensible amount of travel for a short break, so I can narrow my search. (For example, I might want to overlay this with a list of gardens, castles, national parks etc, to come up with a short list of places for a weekend away)

Note that I am not after recommendations of places to go to by public transport from these cities, nor am I after a list of such places. What I'm after is advice on how to work that out for myself!

(This question was inspired by questions like this, but trying to make something more suitable for our style of Q&A)