Back from the trip, time to list the hotels used.
One common thing every hotel had was international power sockets (at least by the desk). I ended up using my euro converter there all the way through. Another common feature was a poor command of English by the hotel staffs, except for one front desk team member (in Via Hotel) but this was a bottom of the low season so perhaps they hire seasonal workers for the peak season and it looks better then. Being the low season also showed up in that invariably I was the only "white" guest in the hotels. Curiously enough, all hotels had thicker blankets in beds - probably meant to counter you blasting the aircon overnight but if you are like me and like to sleep without the aircon, you'll be tossing the blankets, etc away.
Taipei
Hej Hotel Taipei (Da’an Dist). Had their 'Business Room' with a window and it worked out OK. Nothing really to report home about: the room was recently refurbished and had a wooden floor, the bed was an average one, aircon units behind the window, a simple breakfast offered (and some snacks 24/7) in the lobby. Access to/from Taipei Metro is easy as two nearby stations are connected to each other via an underground mall and one of the exits (East Metro Mall, exit 11) is right in front of the hotel (though, it's stairs only = with luggage you might want to use a different exit). The staff had very limited command of English. Compared to what I got, I think this is overpriced. If you get a room for <3,000 NTD per night, then it's closer to what I think it should be.
Via Hotel Taipei Station (Zhongzheng District). Booked their 'Luxury room' to get a window, again. The room was nice and even had a sofa. The room was carpeted but appeared to have been maintained OK (low dust, no smells). The room had been recently done up. A lot of desk space and a spacious shower. Bed OK and all amenities fitted the room well. The only thing detracting was having all six aircon units for the floor right outside of my window and I ended up using earplugs to dampen the noise when sleeping. If you get a room on the street side (or one of the inside rooms with no window), it might be easier. 350 m from the nearest exit (Z10) to the tunnel/mall network connected to the Taipei Main Station and 600 m from Ximen Station (exit 4). The front desk worked well and was helpful. Affordable price and worth the money. Would book again but next time try a street-side room.
Kaohsiung
Holiday Inn Express Kaohsiung Love River (Yancheng District). Of the few HI Expresses I've been to, this was the nicest one. Booked a Queen Standard room but because one of the lights in the room didn't turn off (the switch was faulty), got moved to a King Bed High Floor room. The room was really nice and I wished I could spend a few more nights there. The front desk had very limited English but was helpful and service-minded. The breakfast buffet was rich with options, both local and some western (they are scattered around the room, though, so you should first do a grand tour around to find everything). Three blocks from the Yanchengpu MRT station and within a 10 min walk from Pier 2. The location is outside of the main action but is easy to move around by MRT or by foot. Compared to other HI Expresses I've been to, this one is worth the money. Would definitely book again.