The most comfortable way to get here from Taipei is to take the KuoKuang bus 1879 which usually features seat back televisions and starts its run at Yuanshan MRT station. It stops a few times along the way in the city, notably at the Nangang railroad station and also at the Nangang exhibition center MRT. The final stop is just outside the Nanfangao visitors center and is a great place to grab maps of the area.
Be careful though, because the bus stop before Nanfangao is in Su'Ao which is the closest railroad station to the port, and is also where you'll be able to find scooters, cheap local food, and a cold spring which I've never been inside of. There is a mountain trail beside the cold spring which leads up a small mountain that offers some awesome views of town. Keep in mind a walk between the two towns takes between 20 to 30 minutes, so be sure you know where to get off if you want to rent a scooter. If you don't have a license and want to see everything on foot, the itinerary below is fit for walkers and scooters alike.
Nanfangao itself has several large basins for boats to harbor overnight and at times the place is swarming with fishermen unloading their catch. The U-shaped boat harbors make it a bit inconvenient to see this town on the quick, but if you've budgeted your time well you can enjoy a leisurely stroll. It also allows views down the spine of the boat parking, like this one below.
The main tourist draw is the Mazu temple which is located just down the road from the visitors center. You'll pass by a small set of buildings stretching away on your left and then the land gives way to a boat inlet. The narrow temple next to the 7-11 is your target. It's called the Nantian gong (南天宮) and is host to a gold and jade depiction of Mazu which you can't find anywhere else. It's also got a great view of the harbor below - complete with a maze of dragons on the roof (above) - which is photo op gold.
After the temple you should grab some drinks from the 7-11 and explore the side streets which are packed with restaurants, coffee shops, and stores which have anything to do with fish. Your general target is to follow the main road as it winds its way along the E shaped land mass, stopping in anywhere that strikes your fancy. Because of the high volume of tour buses that stop off here, prices are not necessarily lower than elsewhere but there are great deals and FRESH fish to be had if you're smart.
As you reach the far edge of town you'll eventually be below the east coast highway and facing a large black sandy/rocky beach. There is a small cut through street to Beibing park (北濱公園) which can save you the time of walking around another set of buildings to get to your destination. Tons of people come to the coast here for the view and a coffee at one of the restaurants along the bank, and its a great spot for surf fishing. If you're planning to swim, you should know there are dangerous tides and there are definitely no lifeguards or any means of saving you if you get into trouble.
This is looking south at the mountains where the highway rises up and disappears on its way to Hualian.
The buildings by the small mountains are where you'd head to grab some coffee and relax and take in the view. It's a great place to spend the afternoon just watching and listening to the waves, have a few beach beers, and it'd be amazing to try to find a place that will let you camp nearby.
You can either walk back to town the way you came, or continue along the back side of the wharves via Zaochuan road. This road is a bit empty and industrial although much of it is bordered by the big mountain (大山) on your right hand side. More seafood restaurants line the way here, and it lets out at the far side of the bridge you saw when you got off the bus. There is a pier here which is great for taking photos as well. Sadly, the only time I got here to take a photo it was a bit cloudy.
If you're walking the above can be done entirely on foot, but you should budget a whole day. Be sure to ask in Nanfangao about where to get the bus back to Taipei. If there are problems with drivers not letting you on in front of the welcome center, catch a taxi or local bus (or walk) into Su'Ao and take the bus from there.
Those epic photos you've seen on Google of Nanfangao? They happen up a short ways up the (incredibly busy) Suhua highway at a small turn out with a viewing platform. You should definitely go up here if you have a car, but if you're on a scooter this road can be a bit dangerous because of the amount of heavy trucks.
If you rented a scooter, you can drive slowly through Nanfangao and seeing everything will be relaxing and comfortable. When you're done scoot your way back to Su'Ao and pass through the tunnel by turning right where the port ends and Su'Ao beings. On the other side you'll be in what has become a bit of a nature preserve and is a wonderful addition to your visit.
Inside the nature preserve. You can walk inside along well maintained trails.
The sea as seen from the first turn off after the tunnel.
The park again, in panorama.
The sights on this side of the tunnel are much farther apart, so be sure you have plenty of gas. Get a map from the tourist office in Nanfangao and take your time exploring. Finding the good stuff can be hard - we asked directions more than once - and no one you meet here will speak English. The nature preserve entrance was behind someones house along a narrow pathway of broken pavement. Despite the challenges, each place you get to will be well worth the visit!
When you're all done here, head back to Su'Ao, trade in your scooter, grab a few packed foods for gifts to take home with you - there are a few specialty stores open after dark - and then take the bus or train home. Last time I visited the pickup for the bus to Taipei is separate than other KuoKuang buses which stop here and I wasted at least an hour trying to figure out where to go. Buses stop near the main 7-11 close to the train station. Look hard for the sign because if you're not exactly at the stop, the drivers will pass you by.