As some basic general comments, it is going to be 10-15 years more before Christchurch is fully reconstructed after the earthquake so it remains a work in progress but that shouldn't stop you from going there - it has the best weather of the three cities (although you will be cold in the winter after Vietnam) and probably has more tourism potential than Wellington (so maybe more tourism jobs). However Wellington which is a vibrant little city will definitely have the most hospitality jobs.
I am not sure why you want farm work if you are majoring in hospitality/tourism but perhaps Invercargill would be best there, then Christchurch. (Wellington hasn't many farm jobs!)
For renting look at the site trade me - Invercargill will be cheapest probably by a lot then Christchurch with Wellington the most expensive.
For getting round Wellington is the most walkable and has a good transport system, but not for road biking - Christchurch and Invercargill are good for bikes.