I think that Christchurch to Akaroa ride may follow the Le Race course. http://www.lerace.co.nz/
Some good solid climbs in there, but if you're looking at riding over some passes they won't scare you!
I'd second MillieNZ's recommendations on the tramps, although you'll need to book your spot on the Milford Track because it's fairly popular. It's popular because it's stunning!
Now to go back to convincing my husband to spend New Years in Central Otago with his father ....