Hearst would have had a heck of a time getting Tammany out of the way, as publicly fighting Tammany was suicide even though Hearst was the better mudslinger. Privately, Hearst has enough skeletons in his closet for Tammany to win. Remember Hearst was once known as "The most hated man in America". Spanish American War, agressive business practices, his lavish spending, and... <thinks of term besides megalomania>... his drive to outperform all his colleagues by leaps and bounds in newspaper markets.
In terms of how he would govern, always a toss up. He was never really a deep thinker, and was known to change his opinions often. He would definitely be against corporate corruption, and also government corruption. He would become instantly unpopular with both parties for trying to destroy both of their machines in New York. His business managers: Coblentz (Editor in Chief at the New York American) and Joseph Willicombe (Hearst's Secretary) would be deeply involved in the mayor's office.
Hearst's only hope to be more than a one-termer is to stay incredibly popular with the electorate, and have both parties political machines flounder. This means Hearst will be flinging mudballs every chance he can.
Also I don't think Hearst and Hughes would get along very well. Now then Hearst and Calvin Coolidge? Hearst adored him, and Coolidge got along as amicably with him as anyone beside Marion Davies did.
That's a paradox of Hearst, his favorite president of the 20th century was Calvin Coolidge (He thought FDR would turn Oliver Cromwell on America 1940 and beyond.).
Although since people seem to be asking. Here is how you make Hearst President.
At the 1932 DNC, Hearst controlled Garner's CA delegates. Roosevelt needed them to get the nom. So complicated story made simple Garner named VP by FDR to get the delegates. Garner also said the following quote about the Vice presidency, "Not worth a bucket of warm spit".
The POD, Garner declines becoming VP, Hearst jumps on the opportunity before FDR can retract the offer. Roosevelt has to take Hearst as VP or risk losing the nomination to Smith or someone else. 1932 election goes a little better for Hoover not by much though. Then kill FDR, there you got President Hearst.
No NRA, Big Business style recovery, maybe a PWA, no chance for a WPA. Foreign policy wise, Hearst would stumble a bit, make amateur mistakes, but eventually learn. Expect him to be adamantly opposed to any League of Nations or anything smelling of internationalism, and also be demanding that Europe pay its debts to the US following WW1. He will try his hand negotiating with Hitler, and be utterly disgusted with the man. 50% chance of British-American friendship and lend-lease, odds improve if Churchill is PM (Hearst knew him personally), but expect America to be firmly isolationist until a Pearl Harbor happens. He would dislike France, find Italy acceptable (he and Mussolini got along well), be best friends with the UK, loathe Stalin, side with Japan over China, as long as US interests aren't threatened.
