Christchurch is the biggest city on New Zealand's South Island.
If you're hitchhiking North you'd do best near the Motorway Entrance, but not too close to it, because the traffic entering the motorways moves quickly. There are traffic lights near the entrance, which aid in slowing down cars, and should allow drivers to get a better view of hitchhikers. Get yourself (by city bus or other means) to Belfast which is the suburb on the Main North Road immediately before the start of the motorway. Alternatively take a bus right out to Woodend on SH1 and hitch from the north end of town within the 50km/hour zone.
To get to Belfast take either bus 16 or the 'Northern Star' from the Bus Exchange.
On the map at Liftershalte.info <map lat="-43.514198796857" lng="172.6261138916" zoom="10" view="0" float="right" />
If you're heading South its best to do it from the southern end of Hornby just before the 50km/hr zone ends (just past the shopping malls).
From the center of town, grab the Free Shuttle (Red) until the last stop. From there grab bus 88 to Hornby. You'll get off next to a Robert Norris cafe. Walk to the main street, cross to the other side, and hitch south (HWY 1)!
Heading West you could try hitching from the beginning of Yaldhurst Road at Upper Riccarton or alternatively take the bus (or get dropped off) at the Yaldhurst Road/Russley Road intersection - this is at the start of State Highway 73 but there is a really good area for cars to pull over just past the intersection and before they get up to highway speed.
If you are arriving later in the day without planned accommodation it may be better to ask to be dropped on the outskirts before you actually enter Christchurch. Both highways entering from the north and the south are surrounded by a lot of partial rural and suburban (ie Belfast suburb) where you can either sleep in a paddock (take normal trespassing precautions) or small park. In the morning you can hitch further into the city or take a bus.
If you find yourself in the city centre there aren't really any great areas for camping. The massive Hagley park area is possible but I would suggest just a sleeping bag in some bushes rather than a tent (even though the huge field are tempting) due to the potential of unwanted attention from late night drinkers etc, and the fact that each field is owned by a private entity who won't take kindly to finding you sleeping there.