Q. What are the best databases to use to find an internship in particular manufacturing industry in a specific U.S. city?

Try:

• AtoZ Databases - Choose to search the 30 million businesses and then drill down by Geographic area and then within Business Type for a keyword or NAICS code search.
• 
  Company Dossier  - Choose Create a Company List and then choose U.S., state, city and then search by NAICS or SIC code or business description.