Grab some pamphlets or brochures at Aoraki / Mount Cook Visitor Center. This place has all the info you need to fully enjoy your visit to the area.
You'll have sightseeing choices galore in Mount Cook. Aoraki / Mount Cook Visitor Center is a good place to begin here, but there are lots of other worthwhile places to visit. Sir Edmund Hillary Alpine Centre, Tasman Lake, and Kea Point Walk are close to the tourist information center and will top off your day nicely.