Three ideas.
If one-way tickets are more expensive, buy r/t and use only half. That probably doesn't fit your budget, I would guess. [However, if you do the timing right, you can use the second half of each ticket for a free Tokyo -> Seoul -> Taibei -> Tokyo trip later :-) ]
Buy two separate r/t tickets. Either one Tokyo <-> Taibei and one Tokyo <-> Seoul, or one Tokyo <-> Taibei and one Taibei <-> Seoul, or one Tokyo <-> Seoul and one Seoul <-> Taibei. . I would assume the first is better as the flights are shorter, but the second and third might be cheaper as you have fewer flights out of Tokyo (which is very expensive). But you would probably base this on which way has the best layover. In other words, for the third option, you would fly Tokyo -> Seoul on the first half of one ticket, get your luggage and check-in for your Seoul -> Taibei flight. [Make sure to leave extra time for this compared to a normal connection.] Then after your time in Taibei you fly Taibei -> Seoul on the return of your second ticket. Then after your time in Seoul you fly Seoul -> Tokyo on the return of your first ticket. The downside to this approach is 4 flights (instead of 3 if you used only non-stops), and the layover when you change tickets is a bit dicy if your first flight is late. [If this were a normal connection, and your first flight is late, they will reroute you on a later flight. However, in this case it is a separate check-in, so if your first flight is late, you've missed the check-in for your second flight.]
The other option is to buy a single multiple-city ticket. Go to
ITA Software: Login [login as guest], click on multiple segment, and enter each leg, and see what the prices are. Sometimes it's really good, sometimes it's really bad. [LATER EDIT: I was curious, and ITA is showing non-stops NRT -> TPE -> ICN -> NRT as low as USD1297 for May 5 / 12 / 19. Not sure how that compares to other options.]