I have two weeks of paid leave I need to use before the end of the year, and since no international travel I am looking at nice getaways in Taiwan where me, my wife and my around 1 year old daughter can relax in an affordable but semi luxury hotel with a swimming pool and easy access to a city.
I am thinking November or December for this trip, since prices should be cheaper then, and the weather will be much nicer. Any recommendations?
Try one of the hotels in Hsinchu. They usually rely on international business travel, which is pretty dead these days, so you should get a good deal for a decent hotel with a pool.
My family and I stay at the H20 from us down the street (near Kaohsiung Arena) when we’re going crazy during this shithouse period and want to pretend we’re going on vacation somewhere. 
Rooftop swimming pool with bar, so there’s that!
haha, went to the afternoon tea there at the H2O, I have to say it was soso, prefer many city cafes.
For Tainan, here is good for a few days 台南桂田酒店 (Queena Plaza Hotel Tainan) , North Tainan about 4 hours drive from Taipei.
I had dinner at the H20 hotel. It was a set menu in one of their rooms for just your party. They had a server bring you the food. It was kind of nice having a nice meal without worrying about other people or screaming kids. One of their dishes with the set meal was steak tips. I think that was by far the most tender steak I ever had. Would definitely go back just for that steak.