I just got back from my trip.
In ChCh I was staying in Dyers Pass Rd, so it was a quick pedal up the hill there into the Victoria park area. There's a few great tracks dropping down into the Bowenvale Rd area there, you can happily spend a few hours a day just smashing tracks there.
If you're after something a little bit more scenic and less steep gravity, get out and do the Godley Head trails from the WW2 AA Battery reserve. The first part of it is like a shared walking track, and I had some serious doubts about how good the trail was going to be after climbing up that for a while, but you cross over a fence or two and then shit gets REALLY good, just awesomely rocky trails and features, some brilliant speed and all the while looking out into Governers Bay.
I actually connected out there by riding the Bowenvale Traverse track (also has a track called Lava Flow coming off it that's worth riding) over to Witch Hill. From there you're following along the remains of the Summit road since the quake, but there are few little fun tracks coming off that like Castle Rock that are better than just pounding tarmac, until you get over to the Godley Head track.
Queenstown, make sure you check out 7-Mile. There is also a track out to Bob's Cove, most of that track is a shared access walking track and fairly path beating flat (not an exciting ride, but a pretty one). BUT, when you get out to the end of the cove, the scenic lookout has brilliant black diamond runs (the front is rocky as hell, the back has some more roots involved). The lookout is stunning up there (I'll post a photo later) , if you're after a bit of a leg spinner with an adrenaline hit at the end of it, it's a great track to hit.
I'll edit in some photos later. The CHCH park was still out of action, Trailforks was saying some of the trails were re-opening while I was there, but still massive logging operations in the area, and despite all the signage saying that it was finished as of October, they were cautioning anyone found out there and threatening with trespassing fines.