I'm from Christchurch (although I live in Sydney at present).
The museum has reopened and has some stuff about the city.
However, in the 'container mall' known as re:Start, there's an information center with a lot of info on the history. It's coordinated by the museum and the exhibit/place is 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.
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 ;)).