Haven't been to the base, but looked at the access from Gardiner Hut and Baker Saddle (on the western side of the hooker). It looks a bit epic from the hut, but the view from baker saddle looked better. From memory the glacier fedding off Nazomi is pretty steep around the hut, but then flattens out into more of a bowl below Nazomi. From the hut it looked like you headed up the north side of the ice flow (true right) to reach the upper glacier.
The routes look like some of the nicer rock around the Cook area.
did a route on nazomi a few years ago (nearly to the top)
looked like a good weather day so did it from gardner hut. guidebook said the obvious couloir was grade 2 so we did the obvious couloir (the one that links nazomi to the south ridge of cook). when we got back to the hut found out its supoosed to be grade 4. funny because 2 of us were comfortable soloing grade 4 (70 deg ice) and the other guy thought he'd be ok soloing a grade 2 couloir. think it was bit exciting for him. ....fun times...good route