Multiple/Single visa entry requirments for a US tourist.

You can't get a China visa in Korea because there is not 6 months left on your ARC card. It costs the same fee no matter you apply for single entry visa or multiple entry visa.

You can go to Hong Kong or Macau to obtain a Chinsese visa, then go to Mainland China.

Is there a way to apply for a visa without leaving Korea? I heard Busan has options for people less than 6 months on their ARC cards to visit China. Is this the case?
Or are there any ways to get the visa without having to travel outside Korea to do so?

You can try to apply for China tourist visa through the China consulate in Busan, you can call one of the travel agencies designated by this consulate to check it.

In 2010, as I know, the Busan consulate can issue China L visa to applicants who hold ARC without 6 months remaining validity.

I have been in touch with some travel agencies etc about having less than 6 months left on your Alien ID. The Chinese regulations have been changed recently is what I have been told so it is no longer a simple matter for foreigners to get a visa to China through South Korea. I was told that I would have to go to the immigration office in Gwangju/Busan and get further documents to apply for the visa myself at the Chinese Embassy. They didn't give me any assurance that it would work though. The other option is to get your ID extended but that was not an option in my case (it was tied to my term of employment). Also the Embassy is not open on weekends so if you work during the week then it is near impossible to get out and do the crazy amount of things that are required. This is all information as of November 2011.
(Also, many of the travel agencies in Busan that are listed as designated ones by the China Consulate do not have any English speakers. However, BIE Airlines did and their number is 051-464-1132. The woman was very helpful to me).