I visited Cambridge in December 2012 around Christmas in a group of 3 guys. It's not only a beautiful city with a lot of heritage, it feels pretty safe as well.
We stayed at the outskirts of Cambridge at a Holiday Inn,
Holiday Inn Express Cambridge
Coldhams Business Park
Cambridge CB1 3LH, United Kingdom
It wasn't very difficult to travel around in the city even though I admit it does get a little silent in the night at the outskirts, it was pretty manageable. There were many times we walked through secluded regions without a care in the world. The city centre and the university area is always bustling with joy, so if you can find accomodation near that, it would certainly feel safer and will be more enjoyable.
Taxis run well into the night though in case you feel unsafe. I don't remember the exact rates, but the rates are pretty fair in terms of the standard rates in the UK. I would suspect a 30 minute taxi to run between £12 to £15.