If you have....

 1 day:

Go to the market square. Grab a cup of coffee from Cafe Mobile, to get an energy boost to start the day. Walk out of the market square onto King's Parade, passing past Great St Mary's, the University Church. If the weather is good, consider climbing the steeple to get a good view of the town.

Once on King's Parade,  walk into King's College. Examine the chapel, then walk through the college, and over the bridge, pausing to look at punters below. Continue onto Queens Road, then look back at the iconic view of the chapel. Next, consider visiting St Johns College, which has excellent gardens (as does Trinity), pass past the Wren library, again, visit the chapel. Reappearing on Trinity Street, have a quick browse of the craft market opposite the entrance to Johns.

Turn right, walking back towards great St Mary's, consider walking up either Green Sreet or Rose Crescent for some attractive independent shops. Walking through the market again, visit Tourist Information on Corn  Exchange Street, then onto Downing Street and Pembroke Street., (no, not that one!), via Benet Street and Free School Lane. here you will find lots of the university's smaller museums, well worth spending an hour in. Before lunch, consider visiting the Botanical Gardens (if the weather is good), or the Fitzwilliam Museum (if the weather is bad). Take lunch at a pub or cafe in the middle of town (see dining and drinking for tips), or for a special meal, try Fitzbillies, on Trumpington Road.

Next, down to the river at Mill Lane to burn off the calories from lunch, by renting a punt and travelling through the backs. if you are feeling lazy, consider a chauffeur punt, but be prepared to pay for the privilege. Once back on terra firma, consider walking down to Portugal Place, one of the city's most attractive streets of houses, then again back into the middle of town. Consider doing some shopping for gifts, then write your postcards on the Kings Wall, or in Sydney Street.

2 days:

As above, though take the trip in a more leisurely manner. Also visit the Round Church, the Folk Museum and Kettles Yard art gallery. Try another couple of the museums in Downing Street. For a full list of the University of Cambridge's museums, click here http://www.cam.ac.uk/cambuniv/libmuse... 

Consider taking the city walking tour.

 3 days:

In Summer, consider spending much of your third day punting to Grantchester if the weather is good.

 4 days or more:

Visit the longest pool in the country, the ridiculously cold Jesus Green Lido (open mid May to mid September). Walk down the Towpath towards fen ditton, and watch the rowers practicing for racing (try to time your visit to coincide with a race - town events here http://www.cra-online.net/events/inde... or for college events here http://www.cucbc.org/).

 Consider striking out on the train to Norwich (formerly Britain's third most important city, and steeped in history), Ely (which has an excellent cathedral and is a very attractive market town), Wicken Fen (a nature reserve), Wisbech (a fenland Georgian market town), Huntingdon (market town),  Newmarket (home of horseracing), Bury St Edmunds (a bit like Ely), or London.