Where some cities have a university, Cambridge is a university with a city! The University of Cambridge is comprised of 31 semi-autonomous Colleges, the oldest of which (cleverly named the "Old Colleges") are home to some of the most stunning grounds and architecture the city has to offer. Unless you are visiting on academic business, however, tickets are required for entry.
A stand-out among the museums of Cambridge, the Fitzwilliam Museum owns one of the largest collections of antiquities and art in western Europe. Amazingly, admission is free, however booking is still required to see certain exhibitions.
Within 8 miles of the city center, this former RAF airfield hosts Britain's largest aviation museum. Across 7 hangers, the Imperial War Museum displays over 200 different military vehicles (including tanks and artillery) used by the United States, the United Kingdom, and the British Commonwealth since World War I.
Named for King's College, this pedestrian-friendly avenue is the historic heart of Cambridge. Running from Trumptington Street in the south to the Diagon-Alley-esque Trinity Street in the north, the King's Parade area is home to 9 of the 16 "Old Colleges," countless shops and restaurants, and several minor landmarks (including the tree which allegedly dropped an apple on Isaac Newton's head).