Lots of information via search box.
These will process a visa without requiring you to purchase a travel package. Normally 7-10 days but can be done in as little as 4 days. Prices vary per agency and per country passport.
China Travel Service
臺灣中國旅行社股份有限公司
No. 54, Linsen North Road, Zhongshan District, Taipei City, 10491
02 2562 5858
https://maps.google.com/?cid=3802135005952388380&hl=en&gl=us&shorturl=1
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4 working day processing; HK$1260/US$162/NT$4800
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2 working day processing; HK$1960/US$252/NT$7500; before 9am day 1, return after 3 day 2
STTVisa
勝達簽證通
10450, Taipei City, Zhongshan District, Changchun Rd, 40號6樓之8
02 2541 5271
https://maps.google.com/?cid=17055247359336167738&hl=en&gl=us&shorturl=1
Astor Tours
正達旅行社有限公司
No. 197, Section 3, Nanjing East Road, Zhongshan District, 10491
02 2545 8199
https://maps.google.com/?cid=300501280153729282&hl=en&gl=us&shorturl=1