There are two bus lines that traverse the archipelago, but they only run about once an hour from the main bus station (Chēzhàn) in Makung. Enough Penghu folk will stop for foreign tourists to make hitchhiking viable.
Car, motorcycle and scooter rental places are on and around Chungcheng Rd in Makung. Rates for motorcycles and scooters are generally NT350 to NT400 a day, excluding petrol. Small cars can be rented for NT1300 a day. Most rental agencies require an international or Taiwan licence for cars, but some will let the requirement slide for scooters.
Taxi drivers prefer flat rates to using the meter. A trip to just about anywhere on Penghu will cost NT200 to NT300. Taxi tours can be had for about NT2500 to NT3000 a day.