I am trying to find a resource where I can find the results for historic tennis games, where the match statistics are broken down within each set. The ATP website gives a breakdown for the entire match e.g. Wimbledon 2015 Final, but I would like to know the same statistics broken down by set (or even by game if possible).
The most detailed publicly available professional tennis match dataset I'm aware of can be found on a website called tennisabstract run by Jeff Sackmann. For the information you are interested in I recommend checking out the detailed match reports, which are compiled as part of the match charting project. The "point-by-point" description of a match tells you everything that occurred during each point (including the kind and placement of each shot the players hit).
While they don't have reports on every recent match, they do have 507 mens matches and 546 women's matches; some charted matches date back as far as the 1980's, but the records are heavily weighted toward matches after 2010.
The charted matches can be found in a form more amenable to comprehensive analysis on Sackmann's GitHub page.