Can I apply for China Visa at Consulate Office outside of my jurisdiction state?

I live in Atlanta. The Consulate Office for Georgia is in Houston. The local service agency charges me an additional $80 on top of the $140 application fee to get (regular process) tourist L type from the Chinese Consulate Office in Houston.
I will be in Chicago for a week. The consulate Office in Chicago will be walking distance to my building. Can I walk in with the application, supporting document, current/valid US Passport, payment check or credit card, and an extra passport picture to submit for my application and to pick it up during that same week? (I am aware of the 3-4 days, 5 days, and express pickup options and related fees)
Also, what are the best answers and information to provide on the application to ensure that multiple entries/1-year L type will be granted? I plan to revisit PRC within the next 12 months after my first entry.