7 days?? uh well....depends how fast you drive ;p but, close to auckland is 90 mile beach, or cape reinga (very tip of nz) umm waitomo caves? coromandel...
but ok, dunno if you could do this in 7 days but, start at auckland, drive down east of nz, go to waitomo caves, then new plymouth/taranaki if you wanna check out mt taranaki, dow, down, visit palmerston north is you want, then onto wellington, the capital!! then back up, on the west side, visit napier/hastings, and you could skip that whole right arm (unless you wanna go to gisborne) and instead go straight up, visit lake taupo/taupo, rotorua, then hamilton or tauranga/mt maunganui, and then either thames or coromandel...and then back to auckland :) and if you STILL have time, then i guess, up to 90 mile beach and cape reinga~~~though yeah, this may be a tad unrealistic....
you could just visit the major cities~