Taichung sits in the center of Taiwan's western plain and it's the city, Taichung I mean, that Taiwanese people tend to nominate when you ask where they'd live if not in Taipei - lower cost, better weather, a food scene that competes seriously with the capital, and a design and arts culture that developed in the space left by being the second city rather than the first. The 1969 Blue Sky Hotel sits in a part of the city that reflects all of this without making a point of it.
The immediate area around the hotel is central Taichung in the specific sense of a neighborhood that functions for residents first and visitors second, which is almost always the right situation to be in. Coffee shops that open early, breakfast spots that have been in the same location for a decade, the kind of street-level urban texture that cities develop slowly and can't manufacture quickly regardless of investment. The Calligraphy Greenway is within reach and it's one of those urban spaces that - ask any Taichung resident about it and they'll tell you it's the best decision the city made in the last twenty years.
The National Taichung Theater is about fifteen minutes away and worth going for the building as much as for whatever is playing - Toyo Ito's design is genuinely singualar and the exterior and public spaces are accessible without a ticket, which means an hour walking around the building before or after a meal nearby is time well spent. Rainbow Village is further south and taht specific collision of an old soldier's personal mythology and the surrounding urban landscape is one of those Taiwan experiences that photographs can't adequately prepare you for.
The food culture in Taichung, the food culture here specifically, has been building for long enough that it's stopped being surprising and started being expected by people who follow Taiwanese culinary development - the breakfast shops, the beef noodle spots with specific loyal followings, the night markets in the eastern districts that locals attend rather than the ones that exist for tourism. The hotel sits close enough to the good parts of all of this that a few days of genuine eating in Taichung from this base is one of the better food trips available anywhere on the island.