The University of Auckland

If you are in the city walk through Albert Park and onto the beautiful grounds of the University of Auckland, New Zealand's largest university with almost 40,000 students at this time.  It is smack bang in the middle of the city and was founded in 1883 so has a vast array of both historical and modern buildings/architecture/gardens/art and sculptures.  Start at the Clocktower where you can get a map, general directions and other kinds of useful information.  If you like historic buildings check out the Clocktower, the Old Barracks wall, the old Synagogue, Registry building (where the Vice Chancellor lives), Old Choral Hall, Old Government House, the Old Biology Building, AUSA house, old houses on Symonds and merchant hosues on Princess Street.  For some impressive modern architecture (quite rare in New Zealand) checkout the Kate Edgar Building, Owen G Glenn Building, new biology wing and even the apocalyptic looking maths physics building (apparently it won some architecture award once). 

If you visit during semester there are usually various activities/events e.g. club activities, naked skulls, orientation week, concerts, markets, protests etc as one would expect to see at any good university.  These usually centre around the Quad area where you can also get a cheap meal and chat to the disenfranchised looking natives.  There are plenty of  areas around the Quad to chill-out but I recommend heading to the fourth floor of the student commons where you will find Auckland's best radio station (Bfm) and an awesome student bar called Shadows. 

Other suggestions:
-Take advantage of the massive general library (or the 20 or so other libraries on campus) and its impressive collection to chill out then just take a break and a nap.  The harbour view from the top floor of the general library is spectacular but you wont find anywhere to sit if it is around exam season
-There are hundreds and hundreds of lecture halls around so take advantage of the computers in the clocktower (the rest of the computers on campus require a login) to find a lecture on a subject you are interested in then just sit in on one
-Explore the new business school (Owen G Glenn Building) which is impressive and furnished like a departure lounge with flat screen TVs showing the latest news and what lectures are on where.  There is also plenty of nice art and the university's biggest lecture theatre (the Fisher & Paykel Appliances Auditorium)
-Take a cultural picture in front of the university Marae or Fale Pasifika
-Get lost in one of the the many mazes otherwise known as the Maths Science Physics building, the Engineering Faculty, The HSB building, The Architecture Building or the Computer Science Buildings. 
-Relax on a couch in the basement of the Kate Edgar building
-Find the secret fresh water spring hidden across from the law library
-If you're trying to sell something or meet someone put up a notice in the library basement
-Check out the weird and interesting animals behind glass in the old biology building
-Watch a game of basketball from the second floor of the gym
-If it is summer share one of many grassy lawns with the students
-Checkout the gardens around the Old Government House and the new biology wing