Newspapers.com is the best I have found. They give you a free one-month trial. I stopped using it after that as I don't want to spend that much card money on that site, though it is fantastic.
The Library of Congress also has a great FREE newspaper database, though from what I can tell it is not as good as newspapers.com:
https://chroniclingamerica.loc.gov/
I would also check the libraries, universities, and historical societies (city, county, and state) in the locations that you are looking... if you have a really specific question. Many have free online resources and people to help you with your research, provided it isn't something general like "I am looking for ads in the paper between 1909-1911".
You can also email questions to the Hall of Fame, though those should also be pretty specific. Don't expect a fast initial response, but once someone gets back to you they are very responsive and very helpful (I have done this twice).