Taipei (台北市, táiběishì) is the capital of Taiwan and the heart of the Xinbei (新北市, xīnběishì) municipality, Taiwan's largest. Taipei along with its suburbs is a large metropolitan area with a city bus and subway system (MRT) and connections to the rest of the island via several bus companies as well as high speed and local rail.
<map lat='25.020123' lng='121.489859' zoom='11' view='0' float='right'/>
Highway 1 runs along practically the entire length of Taiwan's west coast, which includes all the island's other major cities. Highway 3 follows a slightly different route down the western side of Taiwan, also passing all the major cities.
Treefrog Has tried three different spots, and the one closest to downtown and with the shortest wait was at Highway 1, Exit 25 in Shilin District (northern Taipei), at 25.079865, 121.513315 (copy and paste that into Google or another map app to see the exact location). It's about 20 minutes' walk from the nearest Metro station (Yuanshan), but you can easily get there with YouBike or by bus (search Google Maps for public transit directions). He stood right inside the pointy tip of the divider between the freeway entrance and the frontage road, and got two ride offers within 5 minutes, turning down the first (to nearby Sanchong) for a better one all the way to Taichung. Make sure to stand right at the bottom of the ramp, not farther back on the main road: Treefrog tried this first, and spent half an hour telling off 10 different taxis without a single free ride offer.
One place to catch a ride westward on highway one is near Deyin Elementary School (德音國小, déyīn gúoxiǎo) in Wugu/Taishan. Many buses stop at this school, the most convenient from the city center perhaps being the 637, which you can catch at Chéngdū Road (成都路) near the Ximen MRT station (西門站, xīměnzhàn), or the 638 which runs from the Nanjing East MRT station (南京東路站, nánjīngdōnglùzhàn) and past Minqian West Road MRT station (民權西路站, mínquánxīlùzhàn).
From the bus stop, take the road just behind you to the east (left as you're facing it, right from the perspective of the bus you just got off) towards Xinwu Road, Section 2 (新五路二段, xīnwǔlù èrduàn), and turn right. Walk 150 meters along this road, being careful because it's essentially an expressway, with no sidewalks and not intended for pedestrians. At the first light you hit, you want to cross the street. Again, be careful, as there's no crosswalk and the lights operate in a funny rotation. Once across, you're looking at the on ramp to highway 1 west. Most traffic comes from the south, so you're best walking a bit to your right and waiting on the shoulder of the curving entrance to the ramp from the south.
Timmy Tofu was picked up from this spot in a matter of seconds, by the very first vehicle that passed.
Treefrog Has also tried the Sanchong Interchange closer to downtown, but gave up after about half an hour (no great place to wait or for cars to pull over). He had better luck at the Tucheng Interchange (Highway 3) near Yongning Metro station. There's a better waiting place here next to a turn lane leading onto the highway, and he was picked up in about 15 minutes by a couple going to Taoyuan.
Ollie caught the blue metro line to Yongning Station (永寧站), exited through exit number 1, then walked along the path pictured below to the 'X' where he stood at the entrance to Highway 3 for only 7 minutes before getting a lift to Hsinchu. From Hsinchu he got a lift after 10 minutes directly to Taichung (See the Hsinchu page for details)