Never been to Cambridge so can't really vote!
My Oxford thoughts are: my favourite bike shop is Warlands, Botley Road. Steve and Andy are great cycling enthusiasts and its a lovely little LBS - hope it's still going strong. My favourite take-way is (or was... haven't lived there since 2014) the south Indian opposite the railway station. Used to do decent basic vegetarian Indian food, dead cheap. My fave sitdown was Sojo, round the corner, excellent Chinese food. My fave museum has got to be the Pitt Rivers - bonkers! My fave walk would be up through Wytham Woods. My fave cycle route would be out up Cumnor Hill and then along to Appleford and beyond. Funnily enough, I can't think of a favourite pub - for some unlikely reason, Oxford's pubs are somehow a bit mundane, beer-wise at any rate... all the obvious 'heratige' pubs are OK of course - White Bear, Eagle & Child yadda yadda, but rather spoilt either by tourists or mediocre beer... odd.
I used to live on a boat opposite Christchurch Meadows - a fabulous spot except at this time of year when the noisey geese would get going with their dawn sqabbles at sunrise...
I was fond of The Bear & Ragged Staff at Cumnor, The Trout at Godstowe and the White Hart at Wytham, but time and modern gastro-pub practices have caught up with them all... Back in the old days only nice middle-class people went out to eat, at posh places like these, but nowadays they're full of every Tom, Dick & Harry, with their dreadful, overweight families... eugh!
The Punter (was The Waterman, landlord ex-college boxing coach, delightfully exccentric...Henry, rather forgetful in his latter years) can be good for food and beer, on a good day.
And of course, the covered market. Meat eater's paradise. John's for bangers, and on Tuesdays - warm scotch eggs; Fella & daughter for inexpensive game, the cheese shop - expensive but top quality and the Stein-endorsed fish shop (Top Tip: visit instead their rather good, modern outlet down the Botley Road, hidden away on an industrial estate