Can AIT help me obtain visas to other countries?  How about visas to the People's Republic of China (PRC)?

No.  AIT is unable to assist with applications for visas to other countries.  For countries that are members of the visa waiver program, American citizens may not require visas for short stays (http://travel.state.gov/visa/temp/without/without_1990.html).  For countries that are not members of the visa waiver program, contact that country's local representative office.

American citizens are unable to obtain visas to the PRC from within Taiwan.  Many people choose to apply for a PRC visa during travel to other countries in the region.  For more information, contact the PRC representative office in the country you plan to visit, or the PRC Embassy or Consulates in the U.S.