Travelling around Taiwan during Lunar New Year

Don't do it. Between Lunar New Year minus three days until a week or so afterwards, trains and long-distance buses are packed with people returning to their hometowns or going sightseeing; room rates in hotels and homestays double or triple (compared with those places' usual midweek prices); famous attractions are extremely crowded; and quite a few restaurants and other businesses close for a few days. Moreover, the roads get very busy indeed.