I love Libraries. I love the smell and the feel of the books. I often say that I would love it if I could be locked in a Library, and just handed food on occasion. Life won’t allow that, and my favorite archives require travel and a hotel. Fortunately there are many libraries and archives that have collections online, and many of them are free.
You will have to decide for yourself the value of a library and its online collection, but here are some examples of what you can find.
New York Public Library has an extensive collection of City Directories
The Library of Congress https://www.loc.gov/ has a great photo collection, as well as databases and records
The Newberry Library https://www.newberry.org/ has a county boundary digital atlas that helps map boundary changes
Danish Archives https://www.sa.dk/en/home/ online includes Parish Registers as well as census and probate records
Access to Archives – Great Britain http://www.nationalarchives.gov.uk/a2a includes Naval service records, RAF combat reports, will and research guides..
The Perry Castaneda Library at the University of Texas https://www.lib.utexas.edu/pcl has a beyond wonderful map collection.
The Archive of the Internet http://www.archive.org has documents, census, records, online books -too much to list here.
Even the small library in the town of your ancestors may hold treasures for you. The nearest library to my small home town is the Delta Utah Public Library. It has links to several valuable online collections, plus a photo collection, and the Beckwith Collection which documents, through photos, the history of Millard County.
To locate a Library, of course, you try a Google Search, but you also should go to FamilySearch at https://familysearch.org. You do not need a sign on to search the Wiki, which is found under the ‘Search’ Tab, on the home page. After you locate the country or state you are interested in, you look for the list of links to archives and libraries for that area.
I could list many more of my favorite online archives, but you need to find out for yourself the ones that are valuable for you.