We share our sports fields with St Catharine's College. The fields are at the end of South Green Road, a 9-minute cycle from Christ's (due to the space needed, central Colleges normally have their sports grounds on a separate site). In reality, of course, if you play a team sport you will play on a number of different sports pitches as you play against different Colleges.
At the fields, there is a sports pavillion, pitches for football, rugby and cricket, and three lawn tennis courts, as well as some hard tennis courts, netball and basketball courts and astroturf hockey pitches.
It's worth also bearing in mind that at Christ's we are lucky to be very close to a number of 'commons' - we have quite a few of these public areas in Cambridge with expanses of grass and a network of paths for people to walk through. You can't play organised sports on commons (proper practices and matches against other Colleges will be on College sports grounds), but as long as there's space (there normally is), you can have an informal kick-about, frisbee, or rounders - the kind of thing where you'd just use jumpers/bags for posts, and you'll see people chatting, reading, running, sunbathing or practicing circus skills etc. there too. Christ's Pieces is next door (and accessible through the side gate) and has handy hard tennis courts, but also has quite a lot of paths and flowerbeds so the better suited space is Jesus Green, which is big and flat with good grass, and is well used when the weather is good (and it also has a skate park).