We always use the Cambridge C&CC site, it's at Great Shelford, about a mile and a half from the city centre. The park and ride is just up the road at Trumpington, or you can catch the bus outside the site entrance.
Or try the CC site at Cherry Hinton, Cambridge - dog friendly - bus into town - pub nearby - also excellent if attending the Cambridge Folk Festival, 5mins walk away.
IIRC, Cherry Hinton aren't taking any bookings until August - can't remember why - upgrades maybe? Although I was told that a while ago so it may have changed now - best give them a call direct.