Cambridge City Council, quite understandably, do everything possible to keep cars out of the city centre.
I usually use the free parking around Grantchester Street and Merton Street and then take walk to the city centre (about 10 minutes) across Lammas Land and along Mill Lane.
Otherwise it makes most sense to use the Park & Ride sites. Parking is free and adults only pay £2.30 each for a return ticket to the city centre if they use the machines at the car parks. (It's £2.60 if you pay on the bus). Each fare-paying adult can take three under-16s with them free of charge:
http://www.cambridges...t/around/parkandride/
If you insist upon driving into the city centre (amidst thousands of suicidal cyclists) you can check the locations and prices of the council-run car parks (which are marginally cheaper than the privately-operated ones) here:
http://www.cambridge....nd-streets/car-parks/
Chris