www.genealogybank.com is very useful. I can also get Proquest online thru a local library database. It has the Times, but also some other cities like Baltimore, Louisville, and Cincy that come in handy in the 1800's.
I find New York World and Brooklyn Daily Eagle to have the best coverage in the 1880's and 90's. Sporting Life is full of news, but beware it has a slant and is not always accurate.
If you join SABR you get "free" access to Sporting News and Sporting Life.