You could walk round the Botanic Gardens and dodge in and out of the greenhouses!

Shotover, in East Oxford, is pretty good when it's slightly damp, because the trees keep you dryish and everything smells fabulous. Can be very muddy if you go the wrong way though. If it were me, I'd either go somewhere liberally provided with pubs (Port Meadow), or somewhere sheltered and close to everywhere else (Headington Hill Park, University Parks). Or give up on the outside and go to one of Oxford's fabulous museums.