London:
Sir John Soanes' Museum at Lincoln's Inn (bizarre architecture, creepy house, superb collection of Piranesis in odd crawl-into room)
The 'Leaky Cauldron' - the Brewmaster pub on Cranbourn Street just off Charing Cross Road - go out the back door and turn left into what I assume was the inspiration for Diagon Alley.
Soho.
Westminster Abbey.
Oxford:
Port Meadow early in the morning with the mist rising (less pretty but more awesome than Christ Church Meadow)
For colleges I'd suggest go from the Sheldonian Theatre under Hertford bridge and down the medieval lane to New College, once in, turn left for the Chapel and cloisters (less showy, but far less crowded than Christ Church) then follow the lane round to take in Queen's, Univ on way to the Botanical Gardens. Alternatively wander north past Wadham (pretty stonework) to the University Museum and Pitt Rivers (both awesome) and take in a game of cricket in the Parks.
Cherwell Boathouse and take a punt up the river.
For pubs, try the Turf Tavern (against the outside walls of New College cloisters down Hell Passage), Eagle & Child on St Giles.
(Not recommending my own college, as it is a bit small and tucked away and better to live in than to visit.)