The Shark is in Headington – a decent walk through residential areas from the city centre.
Oxford University Museum
Pitt Rivers’ Collection (access through the OUM)
Wander in to some colleges
Go in to the Bodleian (even if you can’t go inside and can go no further than the main open quad)
Wander round the Radcliffe Camera and the lanes around Jesus College and Brasenose Lane
then work your way down through the back gates of Christchurch College and on to Christchurch Meadow, then follow the river back to the Head of the River.
There’s also the Univerity Botanic Gardens, the University Park and Punting!
Then explore the hundred amazing pubs Oxford has to offer. Start with the tourist hotspots of the HotR, the King’s Arms, the Eagle and Child (aka the Bird and Baby) then my old haunt of the Lamb and Flag and then the 3 Goats Heads.
100 bonus points if you can find the Turf Tavern without cheating.