The road from Nelson to the coast is very scenic and takes you down the Moutere Valley, through Murchison, Inangahua (Moari for plenty of Whitebait) and the lower Buller gorge. Murchison is a good place for a rest stop and is a small town surrounded by hills. There's also a nice golf course here but no time for that.
The road from Christchurch to Westport is quite a nice one to take and you have two main options. You either go north from Christchurch then go west via Lewis Pass and Reefton or go west from Christchurch via Arthurs Pass and via Greymouth up to Westport. The Lewis Pass route is probably a bit quicker and has a couple of nice stops in Maruia Springs and Reefton. The Arhturs Pass route is nice with a stop in Arhturs Pass and maybe a very quick look at Otira before avoiding Greymouth and straight on to Westport.