If you are staying two nights at Arthurs, how about driving down to Greymouth and the West Coast (about 1.5 hours from Arthurs Pass)?
I am the Director at the Art Gallery in Greymouth (Left Bank Art Gallery), and would love to say "Hi".
You certainly won't be dissapointed with the landscape of the West Coast's rugged coastline (very dramatic on the right day) - and a trip out to Punakaiki (poon-a-ki-ke) is also certainly worthwhile.
The flight over Mount Cook and the Galciers is certainly a 'must do' - again on the right day.
I agree with the earlier posting to your question - with New Zealand's South Island you can't really go wrong!
Let me know when you are going to be in the area?