Mr.Jeremy, Phuket is under the consular jurisdiction of Consulate-General of China in Songkhla, so you can go to Songkhla to obtain a visa. If you go to China for sightseeing, you can apply for tourist visa (L), please submit the following documents to China consulate or entrust someone else to submit it:
1. your original passport
2. one completed visa application form attached with one recent passport photo
3. valid Thai visa or Thai residence permit or other legal entry permit to Thailand
4. sometimes, the travel information, such as the hotel booking and return flight ticket, are required. In most situations, for USA citizens, they are not required.