I’m going to stay mostly in Tainani, I can also arrange to stay in Taipei.
Lasik surgery
In Taipei, I suggest you go to these hospitals & tell them your questions:
(1)National Taiwan university hospital (NTNU)
台大醫院
http://ntuh.mc.ntu.edu.tw/english/
(2)Chang-Gung memorial hospital
長庚醫院
http://www.cgmh.org.tw/eng2002/index.asp
(3)Taipei Hospital
台北醫院
http://www.ptph.doh.gov.tw/English/index.html
In Tainan:
(1)National Cheng-Kung university hospital
成大醫院
http://140.116.253.119/nckm/english/index.asp
(2) Chi Mei medical center
奇美醫院
http://www.chimei.org.tw/
Of course,there are other hospitals in Taipei and Tainan.
About price should ask hospital.

I think you are talking about lasik surgery …I would not recommend having it done there….The safest place in the world to have laser eye surgery done is Vancouver Canada
at least you won’t be blinded there…good luck
References :
In Taipei, I suggest you go to these hospitals & tell them your questions:
(1)National Taiwan university hospital (NTNU)
台大醫院
http://ntuh.mc.ntu.edu.tw/english/
(2)Chang-Gung memorial hospital
長庚醫院
http://www.cgmh.org.tw/eng2002/index.asp
(3)Taipei Hospital
台北醫院
http://www.ptph.doh.gov.tw/English/index.html
In Tainan:
(1)National Cheng-Kung university hospital
成大醫院
http://140.116.253.119/nckm/english/index.asp
(2) Chi Mei medical center
奇美醫院
http://www.chimei.org.tw/
Of course,there are other hospitals in Taipei and Tainan.
About price should ask hospital.
References :