Hong Kong I’d say, but it all really depends.
I wouldn’t budget for less than NT$10k a month, but you can get flights for half that if you’re really lucky. It could be cheap to go to Manila as well, BUT there’s no same day return flight with Cebu Pacific.
Normally Dragon Air is the cheapest option to HK, but China Airlines, Cathay Pacific and even EVA offers deals from time to time that are cheaper. You can always get some cheap flights to Seoul, but again, no same day return flights. Normally a cheap return ticket to HK is between NT$7.5 and 10k, but it’s of course more expensive during holidays (Chinese New Year, Christmas etc), so make sure you book and plan ahead.
Learn enough Chinese to use http://www.ezfly.com.tw and you will consistently find sub-$5,000 cattle class flights to HKG. If you have to stay overnight it’s probably cheaper to use a travel agent with a hotel+flight package.
Dont forget flights to macau on Air Macau or EVA or TransAsia. They are often much cheaper then HK. And if you want to visit HK, its just an inexpensive ferry ride away. Its something like 1200nt roundtrip from Macau to/from HK or something like that. Maybe someone with more current info can chip in on that. I used to fly to macau and back for bout 6000nt (if theres two people it was something like 6500 each for two and includes 2 nites hotel and roundtrip air fare on air macau).
Also try UNi to Laoag from Kaohsiung. They had a cheapie , roundtrip air plus 2 nites hotel for 5000nt.
Also try the new service from Hualian to one of those little japanese islands. read the thread on it on forumosa.
AirAsia offers cheapies to Kuala Lumpur too I hear. And jetstar to Singapore.
China Airlines and Japan Airlines offered 6000nt roundtrips from Taipei to and from Okinawa (back in 99 so pls check current prices) right from their offices.