Click on photos to enlarge.
Notes in italics from Oxfordshire by Jennifer Sherwood and Nikolaus Pevsner (1974)
Yale University Press, New Haven and London.

Robertof Eglesfield, a Cumberland man, chaplain to Queen Philippa, established The Queen's College in 1340 ... Whatever was built in the C14 and the later Middle Ages ... has been swept away, and Queen's is the only old foundation with no buildings at all prior to the Restoration.  

Front Quad (mainly 1709-34, possibly by Hawksmoor) is the grandest piece of classical architecture in Oxford, and it belongs to the short phase which one has a right to name English Baroque, i.e. Baroque with English reservations. The High Street in particular has nothing as rousing as the screen of Queen's; for the quad is open to the S in no more than a screen with a domed gatehouse ... Tuscan columns, two deep, and set diagonally with their own slabs of entablature, carry the dome. The statue of Queen Caroline is by Henry Cheere. ...

The North range of Front Quad in which a middle gateway has on its l. the hall, on its r. the chapel. ... The arched windows are set high up and separated by giant Tuscan pilasters. The windows themselves appear to stand on very high, totally unmoulded pedestals - a way to suggest layers of wall different in depth. The centre has giant attached Tuscan columns and a pediment with a figure composition. ... A cupola on top with diagonally set pairs of columns. ...
Last picture: The apse of the chapel ... with the windows set back slightly behind the sheer wall surface ...

The earliest building is the Williamson Building, i.e. the E range (of North Quad). It was built in 1671-2, ... and Wren concerned himself with the contract, the measurements, and the design. However, of that design we do not have much, since the building was lengthened and heightened and to the quad (not shown) totally remodelled in the C18. The original work is the short end to the N  towards Queen's Lane (second and third picture). It has cross-windows, and the centre is a blank niche.
The range beyond the Williamson Building is of c.1707.

A glimpse of the library, occupying the west side of North Quad. Erected in 1692-5 with arched windows.

There are no pictures here of the interiors of the quads since the college is not open to the public. However, there are views of the quads and the interiors in the 'virtual tour' at The Queen's College Website.