We did the same with our 9 month old. We drove from Christchurch to Oamaru, Dunedin, Te Anau, Milford Sound, Queenstown, Mount Cook, and Akaroa. Every town had a playground so it was easy to stop and grab a bite and get fresh air. We stayed in places like Te Anau Great Lakes Holiday Park and it worked nicely, though it was hard not to collect points.

More recently we took our 10 month old son to Slovakia and it was also great. We drove quite a bit there, too, and it was similarly kid friendly.