Best as in…scenic? Not a lot of people? Easy?
I personally don’t like the Roahe to Tamsui route because after the Beitou area, the path narrows and if it’s later in the day, you tend to get a bit paranoid of wether people will stay riding (or walking) in a straight line.
Personally, I like the route from Raohe Night Market --> SheZhi peninsula (the duck head) https://goo.gl/maps/JPRvDzaCrXM2 --> double back and cross SheZhi bridge (https://goo.gl/maps/YnEevhL3WG12) --> head back southeast towards Grand Hotel --> XiZhi where the bike path ends (https://goo.gl/maps/kET5Z7b2aNJ2) --> Rao He
I haven’t done the math for the above route, but it should be enough.
You can give these roads a try (ranked top to bottom, easy to difficult).
Jian Nan Rd - https://www.strava.com/segments/752220 - this climb will be over before you know it. We normally use it to skip going through the tunnel during busy hours.
Zhong She/Shooter’s Hill - https://www.strava.com/segments/1761462 - one of the most ridden roads in Taipei, it’s a great beginner road since there’s only one section where the gradient kicks up to to a higher gradient, but only lasts 50m or so.
Feng Gui Zui (FGZ) - https://www.strava.com/segments/641218 - FGZ is actually one of the most famous climbs in all of Taiwan. People have come all the way up from Tainan just to ride FGZ. Why though? My bet is FGZ has every type of climb all thrown into one 6km segment. If you’re looking for something a bit longer/difficult than Jian Nan and Zhong She, FGZ is your best bet.
Wu Zhi Shan - https://www.strava.com/segments/802344 - The start of this climb is the closest to Rao He, but you will have to ride through Neihu to get to the base. It’s longer than the FGZ segment, but personally, I don’t think it’s as difficult as FGZ. You’ll start the climb with a few kickers, but it’ll flatten out halfway and you’ll be riding through lots of hair pins. This climb is one of my favorites because there’s a sweet view at the top with a few coffee shops to choose from.
Any time after 10-1030AM is a good time to descend from the above climbs. You may bump into one or two cars going down, but most of the cars will be going up. We normally descend from FGZ and/or Wu Zhi Shan around that time and it’s a 50/50 chance we descend behind cars. However, for these routes, I wouldn’t be too concerned about actual traffic.
Good luck, have fun, stay safe! Feel free to ask more questions if you have any!