Visit Fitzwilliam Museum (free and just the right size for a short visit)
Visit Botanical Gardens - just outside the city centre but very peaceful
Take an open top bus - a bit naff but gives you a good appreciation of the whole city
Visit the American WW2 Cemetary just outside the city - open top bus stops there
Visit some colleges - those outside the very centre of the city are more likely to be open to visitors so avoid Kings, St John, Trinity, Clare
Have dinner or coffee and cake at Fitzbillies