A very dated museum, but it's only 5nt and you get a postcard in which you can put a couple cool stamps on. The best part of the museum is the floor where they showcase stamps from all around the world even from small or unique countries. However this is definitely not a place you take a kid, super boring for them and very dated.
I thought that an hour would be enough to see the entire museum but I ended up staying for almost three hours. I was pleasantly surprised to see a comprehensive collection of postal artifacts not just from Taiwan but from many countries, including those that no longer exist (e.g., South Yemen). The interactive stamp designer, which lets you create a commemorative stamp with your picture in it, was a neat idea.
There is a small admission fee of 5 NT dollars. Most exhibits are described in both Chinese and English. All of the museum employees I interacted with have limited English.
The place to go if you are into Taiwan philately history.
Behind the museum is Guling street, where there are several philatelic shops and worth a visit as well.
Umm... Not interested in but very educational.