I stayed for a month at Kate's place two summer's ago, and this summer I returned for another month. Coming back to Kate's was like coming home. It was just as comfortable as I remembered it to be.
Working with Kate was great. When a lightbulb blew on the terrace she came by the next day to replace it. When the battery on the water heater needed replacement she was there within hours with a new battery.
Despite what other guests have written, I had no problems at all with mosquitos. In addition, walking up and down the 4 flights of stairs several times a day was really not a problem, and I am 61. One of the nice things about the place is that it has a working stove, so with a supermarket right downstairs I was actually able to prepare some meals at home. Other Taipei Airbnb flats I've stayed in usually had no more than a hotplate.
You should know that the neighborhood is pretty sleepy, and almost all the restaurants on the pedestrian street close up by 9. But there are plenty of late night fast food options if you head up to Roosevelt street, and the night market at Gongguan, a 5 minute walk, offers more options.
There is a Starbucks right around the corner, the Taipower MRT subway station is just a 5 minute walk, and for you gym rats there are two options, a World Gym by the Gongguan MRT stop where it is possible (although complicated) to get a short-term membership and the NTU campus gym where you can get a cheap short-term membership. And if you are a jogger, the NTU campus has a nice outdoor track.
In conclusion, this is a comfortable place to stay, especially if you plan on staying more than a few days. It's close to subway and buses, supermarket and banks, restaurants and cafés. I look forward to my next stay.