I'm from Christchurch.
The museum has reopened and has some stuff about the city.
There's an information center with a lot of info on the history. It's coordinated by the museum, and (I gather in collaboration with them), an exhibit/place called Quake City. It has an interactive exhibit on the city, the science of the quakes, the damage and the rebuild.
The tourist tram is operating again, and it'll take you through the heart of the city and see a lot of the damaged areas.
You could also get a bus/drive out to New Brighton, a lot of the roads are still fairly awful, but if it takes you through the Red Zone - it's a couple of entire suburbs that have been removed. As a result there are still powerlines/roads but no houses! The area is being gradually converted to a large natural area along/near the Avon river, and foraging is already quite an activity in there.
If you want some preparation work, try and watch "When a City Falls". You can see the trailer online. It's a documentary iniitally about the first quake that didn't do much damage, but then when the big one hit, they ran into the city as others ran out, so the footage is incredible. It's very well done and most of my Christchurch friends found it very good, if a bit upsetting to recall the events of the day. (Also the small aftershock we had in the cinema while watching didn't help).
Nobody is going to really criticise you taking pictures of the Cathedral and other damaged landmarks. One of the biggest things is that Chch has lost a lot of its heritage, and as a result, photos that document the before, the during and the after all help.
Enjoy it, and try some Dmitri's Souvlakis, the best street food in Christchuch (and my old neighbours ;)).