A prominent peak in the lower Tasman Valley standing at 2749m, the Nun’s Veil definitely has an aura about it, especially with horrific notches and jagged choss-piles accompanying its skyline. The Gorilla Stream Route is an excellent grade 1+ summer mountaineering trip, easily completed over a weekend.
Glacier Explorers water taxis can be used to jet across the Tasman Lake in exchange for some beers. The approach via Gorilla Stream remains true to the Mt Cook region, involving several long sections of groveling interspersed with the usual thirsty stream-bed slog. A good camp site can be found at 2270m in preparation for the summit push. Grade 1+ steep snow climbing takes you to the summit with great views of the Aoraki region. Return via the same route.