I stayed in Livingstone.

It has more services, but it requires a taxi ride to the border and a walk across the bridge to get to the falls.

Staying on the Zim side leaves you within walking distance of the falls, and means you don't have to visit Zambia at all. Saves a bit on visa fees.

Which airport you use might determine which route to take, as, at least when I went, there weren't any specific reasons to choose one location over the other.