Cambridge, especially Old Cambridge, is a wonderful amalgam of the ancient and contemporary. The university (I believe there are 38 colleges - not sure about that) is spread out all over the north side of town and is rich with history. And don't forget to try out the punts (like gondolas) on the Cambridge River while in the neighborhood of St. James College.
Also, don't forget you are in a college town and so expect to be awash in young people, which makes evening pub life rather lively around the colleges.
OK, here's a quick Cambridge trivia question: What are the three most popular forms of wheeled transportation in Cambridge?
Answer: The car, the bicycle, and the baby carriage (or pram, as they call them). Like I said, it's a college town and that includes a coed student body and lots of 20-something grad students. Do the math.
I recommend visitors room a little south and walk through the town every day - don't stay too close to your destination in other words, or you'll miss too much. Nothing is far away, and the only thing taxis are used for is hauling tourists, parents, and their luggage to and from the train station.
As a semi-permanent fixture at a number of the university's libraries, I can attest that the people who work in and around the university are quite charming and quite tolerant of the occasional American academic curmugeon (as I) who needs directions. Fear them not in other words.
The food is, well, British, so don't expect much. The post-sunset local (non-university) pubs are, well, British, so don't expect much there either. But if seeing Old Cambridge and the hundreds of little shops and markets that service its community sounds fascinating, it's only a short train ride from London's Waterloo Station (NOT Paddington).
Bring your camera!