What would the weather be like end April until early May? Am planning to visit Taiwan.

It will be 70 F to 75F during that period of time. There will mainly have sunny days.
Do you refer to the distance from Taoyuan Airport to Hualien? If yes, it is around 134 miles (215 kilometers). About the transportation, upon landing, take shuttle bus to Taipei Railway Station.
After arriving, there are several direct trains that can take you to Hualien.