We were in Taipei with a 3 month old in Jan, and didn't miss NOT having a stroller and would avoid it if you feel you can (which you'll need to decide based on your kids; obviously mine wasn't running away ;D). It seems almost nobody in Taipei and I can see why - the metro stops are very nice, and I believe every station is wheelchair accessible so you're good there, but the trains and stations get PACKED, and the sidewalks in many parts of the city aren't particularly wheel friendly ((new taipei city; taipei proper is much better) my dad requires a wheelchair so we saw that first hand).

Our backup plan, if we decided that we needed a stroller, was simply to purchase a cheap one while there, but we didn't end up doing that.