Nantou (南投) is a city in Nantou County.
There is a bus station right by Carrefour that connects to all major cities around Taiwan.
Downtown Nantou (mostly the shopping district) is small enough to get around on foot.
The easiest alternative mode of transportation would probably be by taxi. Near the bus station and Carrefour there are always taxis standing by, but since these usually don't use meters, be careful and negotiate a good deal first.
Every Wednesday night, there is a night market on the streets around Carrefour.
Nantou is famous for delicious Taiwanese dishes.
Refreshment shops can be found all over, most offering a variety of bubble teas, tea, and fruit juice.