Hi there. I agree with previous post. Really good idea to visit a tower closest to you. Where do you live? I may be able to give you a contact there. I am up in CH TWR so would be happy to show you up there if you are in CHCH. Spending a few hours in a tower is invaluable for the selection - gives you some good advise and is also qudos for the interview.
It's been a while for me but some of the tests I remember are memory type, recognising patterns (in number/letter combinations), spatial orientation (unwrapping cubes, predicting paths in 3D etc). Computer tasks again test spatial awareness, multi-tasking, prediction etc. In the group exercise they look to see that you can work in a team but are not too reserved or too domineering.
Hope this helps. I would say that Airways should have a course or two running in 2013 so good luck, and if not sucessful the first time take notes of the tests and don't be afraid to apply again if Airways tell you that you were close but not sucessful. I know of people that applied 3 times before getting accepted.