Taichung High Speed Rail station is the connection point for most visitors arriving from Taipei or Kaohsiung - the HSR takes about 50 minutes from Taipei and the station sits in the western district of the city, about 20 to 30 minutes from the hotel by taxi or MRT depending on traffic. Taiwan's HSR is the kind of infrastructure that - once you've used it you understand why Taiwanese residents treat the island as effectively much smaller than its geography suggests, and the Taichung connection is efficient enough that day trips from Taipei are genuinely common.
Taichung Airport handles some international and domestic routes but the main international entry point is Taoyuan near Taipei, from which the HSR connection south to Taichung is the most direct option for most travellers. The journey from Taoyuan to Taichung HSR station takes about 40 minutes and the whole process from landing to hotel is manageable within two hours if connections are running normally.
Getting around Taichung itself is primarily by taxi and Uber, both of which work well and are cheap by international standards - the city has a YouBike system that locals use extensivley and which is genuinely useful for the flat central districts. For destinations further from the center, taxis and Uber are the realistic answer and - the fares across the city are low enough that a week of taxi travel in Taichung costs less than a single airport transfer in most European cities.
The Taichung MRT green line covers useful routes through the western and central city - the oriignal stations on the line have a design standard noticeably higher than most urban metro systems, which is typical of Taiwanese public infrastructure and never stops being slightly surprising. The airport bus connection, the bus from the city I mean, runs to Taoyuan and is worth knowing about as an option for departures rather than going back via HSR if the timing works better.
Parking in central Taichung is limited in a way that - the streets around the hotel weren't designed around the volume of cars that now use them and the hotel can point you toward nearby options but can't solve the underlying geometry.