Being a stay-at-home mom who lives in present-day Ohio but writes fiction primarily set in New York Century at the turn of the 20th century, I rely heavily on Web-based history resources. Here's a list of my most-used sites, and insight on how I employ them.
Google Books: While the Google Books project has been the source of contention for many in the publishing industry lately, their publications which fall in the realm of public domain can be a big help for researchers. Using the 'Advanced Search' feature, you can look up search terms within specific dates. You can search full texts of public domain books and even download most in PDF or EPUB formats.
New York Times Archive: Using the 'Advanced Search' function, you can search any day's release of The New York Times from 1851-1980, with specific dates and search terms. When I first started doing historical research, I lost eyesight on microfilm archives of this paper at our local library! Each article is viewable as a PDF download.
Library of Congress American Memory Project: This is a massive resource with collections ranging from Advertising to Women's History, African-American History to War and Military History. It takes a bit of time to navigate, but chances are if you're looking for very specific information, it's in here. The most fascinating of these fully viewable online collections is the Thomas Edison films of New York City.
Cornell University Making of America Archive: A digital library of primary sources in American social history from the antebellum period through reconstruction. The collection is particularly strong in the subject areas of education, psychology, American history, sociology, religion, and science and technology. This site provides access to 267 monograph volumes and over 100,000 journal articles with 19th century imprints.
Museums' Virtual Exhibitions, such as The Museum of the City of New York: The great thing about singular museums' exhibitions is that they change on a somewhat regular basis.
The Dictionary of Victorian London: Historical thriller author Lee Jackson has collected and organized articles and info regarding life in Queen Victoria's Britain. Includes unique maps! Even if you don't write in this period or time, it's definitely worth a look.
The Inflation Calculator: Need to know how much $5 meant to a person in 1816? A simple "form adjusts any given amount of money for inflation, according to the Consumer Price Index, from 1800-2007."
Small sites: One of my most-referenced sites right now is No. 9 Duane Street, which is chock full of info about the newsboys' lodging houses of the 1800-1900s.