Hope this helps.
Taipei - Hualien
Can ride 2 routes. I’ve done both on big motorcycle multiple times. Either way is a long day coming from Taipei. Start early. Rest along the way. Don’t go if weather is bad, it’s dangerous, and better to enjoy ride and view with good weather. By the time you reach Hualien, you’ll be dying for a hotel so have it ready for you when arriving.
along the coast past Suao. Will already by tired by the time you reach Suao. Lot’s of trucks trying to kill you along the coast. Just stay away from them. Stop often for pictures which people in cars can never do.
through the mountains past Wuling Farm, Lishan, and down through Taroko. Beautiful, few vehicles. Not many places for food, so stock up and hit 7/11.
Hualien - Kending
-Beautiful ride on Highway 11 along the coast to Taitung. Not much traffic, not many trucks.
-Taitung going south on Highway 9 along the coast, not so great but some decent views. After you start going up into the mountains on turn on 199 for beautiful scenic ride through mountains. Little traffic. They have choice of 199 to 26 on into Kenting via Hengchen where you’ll eventually be on big roads again, or 199 to 26 to 200 which is more scenic. Departing Kending going to west coast will go through Hengchen anyway so no need to do it twice.
Kending - Tainan
So many routes. Take your pick on roads and sights. To avoid competing with traffic, go through Pingtung county area.
Tainan - Taipei
So many routes. Take your pick on roads on sights. Mountain side or ocean side. Up through Chiayi county into Changhua is interesting. Highway 3 starting on east side of Taichung all the way north is very popular for motorcycles.