Penghu's not the most wired of places, but most hotels and guesthouses in Makung offer wi-fi connections.
The Bank of Taiwan has a foreign-currency exchange and ATMs.
South Seas Tourist Service Centre provides information about Chimei, Wang'an and Tongpan Islands, as well as boat tickets. It also provides a free left-luggage service.
The main tourist information centre is not easy to access, so pick up travel brochures at the airport or ferry terminal travel kiosks. Your best source for boat and plane schedules, and other information, will be your hotel or guesthouse.