You will be doing he Haas Pass the easy way and miss out on the glaciers, past them it will not be so wet.
Though the Ale trail aka Otago rail trail is good, watch out for the Tiger Hill at a massive 1:50
And the Otago peninsula is stunning and in Dunedin there is the steepest road or street in the world, good fun having a go at.
Any were you go is great, or pop up to Mount Cook, great DOC campsite there and At Lake Tekapo the oldest church and a great place to look at stars and the colours of the lake etc etc