Alexander Hamilton had great success and helped build the United States, but by the end of the 1790s he told a friend that there is no place in this country for me. Why did he feel this way?

Hamilton was beholden to an increasingly hostile political environment. Ironically, he would prove to be ahead of his time -- modern America is almost entirely build around the Hamiltonian conception of the Constitution, the Economy, and the role of government, rather than its Jeffersonian counterpart -- but, at the time, the fledgling Republic was sympathetic to Jefferson's populistic ideals.

Hamiltonianism and Jeffersonianism, while not being comparable to modern political ideologies, being products of a distinct time period (the Age of Revolution and the Industrial Revolution), were part of an ideological battle that still, to some extent, plays out in different forms today.

Obviously, upon America's conception, there were two main parties: the Democratic-Republican Party, and the Federalist Party.

The Federalist Party (Hamilton) was, above all else, staunchly capitalistic. Almost all of its stances, be they "progressive" or conservative, stemmed from this fundamental embrace of market forces. They strongly supported American industrialization, urbanization, free-market ideals, and the consequences of the like. Some of these consequences seem strangely progressive to the modern-day observer but are in fact natural results of the free market -- a relative openness towards minorities (after all, someone's race or place of birth doesn't affect the bottom line of the business), centralism (free trade would need a robust government that could protect property rights), heavy defense spending (to ensure American commercial interests), and tolerance towards immigration from the Caribbean (free movement of labor) are a couple examples. Obviously, some policies were unrelated to this core economic tenet (dogmatic patriotism, firm religiosity), but to understand the essence of the Federalists, all you need to know is that they were extreme capitalists -- at a time, mind you, when Adam Smith had scarce been published for twenty years.

The Democratic-Republican Party (Jefferson), on the other hand, was equal parts reactionary, populistic, and almost proto-socialistic. I think that the best modern example one could give here would be Huey Long gone libertarian, but it's really hard to map this ideology to modern terms. Essentially, the Democratic-Republicans were pining for the "good old days", and the "common man" who had been left behind by the new industries springing up daily in New England and the mid-Atlantic area, promising to protect their interests at all costs. This meant a lot of different things, but above all it meant representing the agrarian plantation interests of the South as well as the settlers of the frontier areas. Since the Federalists were capitalists, the Democratic-Republicans defined themselves in opposition to free-market capitalism -- they didn't have a clear economic stance, but they vaguely supported the Southern plantation system, imagining a nation of self-sufficient farmers rather than industrial traders as being the gold standard. They staunchly opposed government "overreach", the supposed "depravity" of federal policies, but didn't have all that much to support -- their agenda was largely negative, defined by fears rather than hopes.

Now, as you can guess, the lines for these parties were largely regional. The capitalistic, urban, relatively modern North tended to vote Federalist, whereas the South would vote consistently Democratic-Republican (also important to note is that the Federalists were far more consistently the party of abolition). Because of simple demographics, the South would normally win that debate (Pennsylvania would normally vote with the South despite being geographically Northern) -- the standard tally puts the South at 78 electors to the North's 61. Unless the Federalists would manage to hold onto every single one of their states, and flip at least one major Southern state (like Adams did in 1796 with Maryland), they had no real chance at winning.

Their saving grace, however, is that the single most important man in the nation -- George Washington -- was standing behind them. Officially nonpartisan, Washington was a Federalist in all but name, and this was clear to practically any political observer of the day. Hamilton, therefore, was the primary driver of Washingtonian policy -- hence his "great successes" that you mention.

However, policy success never really changed the fact that his party got screwed over by demographics. John Adams eked out a win in 1796, but that was really because of his status as Washington's deputy, not because of his ideological leanings. Indeed, when the "Washington Effect" wore off, Adams lost decisively to Jefferson (61%-39%). The fact is, Hamiltonian capitalism just wasn't an easy pill to swallow for agrarian Southern interests.

And that's what Hamilton meant when he said the country had no place for him anymore. His ideas had been vilified by a demagogic opposition, he was reviled in large swathes of the country for being a "crafty, capitalist Northern merchant", and was seen as a symbol of extremely threatening modernity. Politically, his beliefs doomed his chances of ever becoming President. He would be vindicated after the Civil War, when America would once and for all resolve the agrarian-industrial conflict in the latter's favor, and his legacy would be rehabilitated by those very same Northern urban dwellers who now controlled the levers of power in the nation and made up a majority of the population -- but at the time, not so.

Edits:

Thanks for all the love and appreciation, guys! Really made my day :)

I just wanted to address a couple things in the comments:

1.) The 'socialism' point: A lot of the people in the comments section are disagreeing with me on this one, for various reasons. I just wanted to clarify that when I called the Democratic-Republicans a "proto-socialist" party, I was not really referring to the formal ideology as introduced by Marx and later furthered by various ideologues throughout the world. I am talking about 'proto-socialism' in a more general sense of leftist, populist, reformist (as opposed to revolutionary) rhetoric, in the same way that many historians have counted Tiberius Gracchus as a proto-socialist.

2.) Tariffs are anti-Capitalistic: Several have made the point that the Federalist party actively supported what were in effect anti-free market policies, such as using protective tariffs and government planning in order to advance American industry. I would argue that such measures were meant to be temporary stopgap solutions rather than something expected by the Federalists to be permanent measures. Perhaps, policy-wise, the Federalists did not always follow the principle of maximizing freedom in the market, but I think that the vision that they pushed for America was certainly one with a laissez-faire economy -- and, in my humble opinion, I think the latter is more important to the question (ie the public's qualms with Hamiltonian ideology).

3.) Democratic-Republicans were capitalist too: I find this point to be extremely murky, in no small part because of the fact that the party itself was so divided. In making the point of Jefferson's anti-capitalism, I would cite Chomsky in Ch. 6 of Understanding Power: "Jefferson did not support capitalism; he supported independent production… The fundamental Jeffersonian proposition is that ‘widespread poverty and concentrated wealth cannot exist side by side in a democracy." Now, Chomsky being critical of capitalism throughout the book means that he has incentives to overplay Jefferson's anti-capitalist tendencies, but nonetheless, I find the second part of the statement, about "widespread poverty and concentrated wealth", to be consistent with every source I have read. Also, obviously, he is a prolific historian. Since Jefferson was the leader of the party, it would be safe to at least assume that a large contingent of the Dem-Reps would have similar misgivings to one of the fundamental hallmarks of modern American capitalism. Also notable are his opposition to creating a Central Bank and providing sources of reliable credit.

Feel free to contest anything above: after all, I'm neither American (im indian) nor a historian (C++ programmer).

Also, two more things that I would like to reiterate that others have said:

u/fearofair and u/AffixBayonets mentioned that I didn't talk about centralization of government and the strength of the Federal Government in my answer. Sorry, I was just tired and forgot! Of course, one of the most important points in the struggle of the First Party System (possibly even more important than the agrarian-industrial dynamic I mentioned) was the fact that the Federalists supported a strong central government, whereas the Republicans supported as limited of a federal government as the Constitution would allow. That also wasn't great for Hamilton, since he was alive at a time when American libertarianism was perhaps at an all-time high, and his pro-government sympathies won him much scorn.

u/PhD-Holder-Nordic also mentioned something super-important: Hamilton's personality itself. He could certainly charm the right people, no doubt, and he had a youthful vigor to him during the years of the Revolution, and he was widely recognized as being prodigal, but he had a condescending way of speaking to others which made him disliked. Add a certain absolutism, brashness, and an unwillingness to compromise, and you get a person who was disliked by many not because of his policies but because of his demeanor.