You're right, from a strictly abstract perspective, Nixon did succeed in several important undertakings. Unfortunately, Nixon sort of 'poisoned the well of democracy' as I think of it, and, in conjunction with that, most of his accomplishments tend to raise questions of whether the ends justify the means.

For example, while the moon landing did occur under Nixon, most of the funding and development of the program had occurred throughout the last decade or so. I believe Chris Wallace specifically addresses the moon landing in Kennedy and Nixon: the two began friendly and ended up as rather bitter rivals, so it came as a bit of a personal victory to have Kennedy's program brought to fruition under his administration.

Going further, the relations with China that were opened occurred in light of the Indo-Pak war. Have you ever heard of Archer Blood or the Blood Telegram? Pakistan, during the Nixon presidency, was on friendly terms with both the US and China; when they began committing genocide on their own citizens, from Hindus to university students and professors, the Nixon administration, under Nixon and Kissinger, turned a blind eye until India under Indira Gandhi had to step up as prime minister of India and prevent the genocide. As Gary Bass discusses in his book The Blood Telegram, this is not like FDR not taking action to prevent the Holocaust in World War II; there was no question of the US possibly intervening. We already had intervened, on the side of the dictator by providing weapons and support for his genocide. This was the price we paid to open doors to China; we couldn't upset Yahya, so we turned a blind eye to genocide. Pretty damning against Nixon.

Nixon's desegregation of schools was more on the surface than anything; Rick Perlstein discusses Nixon's alliance with Strom Thurmond that helped to impede the progress of integration. Nixon is the same guy who also, as Perlstein records, appealed to Iowan farmers by telling them that well-known pacifist Martin Luther King Jr. was training black militants to kidnap and rape their daughters.

I'll address the Vietnam War last, but prior to that: Watergate. Opinions are divided on this, and the problem with Watergate is that it's a long, convoluted affair. It involves a lot more than him being caught being unethical: Nixon was caught authorizing sabotage tactics throughout the 1972 Democratic primary to ensure that George McGovern, considered the least viable democratic candidate, got the nomination. Imagine if Trump had orchestrated throughout the 2016 primary campaign via various underhanded tactics to ensure that, say, Lincoln Chafee got the nomination this year, instead of dropping out after the first democratic debate. Especially if these tactics included false mailings, innuendo, cash bribes, you know, a lot of things that are explicitly outlawed and surpass the level of "aren't most politicians corrupt?" in the opinion of many.

Then, upon being caught, Nixon refused to subject himself to the process of an independent government requiring checks-and-balances: he tried to apply the theory of executive privilege and national security to his own sabotage of other political parties, rather than coming clean. When pressed by Congress with subpoenas, he only grew more belligerent. Perlstein, again, records in The Invisible Bridge, fears that toward the end of his presidency, Nixon would rather rise up in an armed insurrection to keep the presidency than submit.

The Vietnam war, in fact, did not end under Nixon, as it concluded in April 1975, under Ford. Nixon, though he ran on a platform that called for Vietnam to be removed as a subject for debates, he simultaneously convinced his agent in Paris to sabotage the Peace Talks, with South Vietnam beginning to pull away and demand more whenever North Vietnam made concessions. His aid told the North Vietnamese to hold out as they would receive a better deal under Nixon.

After being elected, Nixon, continuing the policy of LBJ, accelerated bombing and tried for the "knock out blow" against Vietnam, which resulted in covering the ground with what has been estimated as enough steel to pave the entire country over to roughly three-eighths of an inch, putting together the calculations of General Harold K. Johnson.

Whenever journalists reported to the war zone, they similarly returned with devastating accounts of prisoners of war held by South Vietnam as 'skeletal masses of flesh' while it is reported that torture in North Vietnamese prison camps ceased in 1969. The US and our allies in South Vietnam also held a disproportionately high number of POWs: not only was our treatment of POWs worse on a level of magnitude, we held more people as POWs with a similar degree of magnitude.

While Nixon made efforts to paint those opposed to Vietnam as the minority, even reviving the Silent Majority phrase for this purpose, the Moratorium to End the War in Vietnam, which a young Bill Clinton participated in, clearly showed that the peace movement had gained traction with a larger portion of America than a liberal fringe.

In addition to all of this, Rick Perlstein makes a convincing argument that Nixon allowed civilian dikes in Vietnam to be bombed, which resulted in the deaths of a million of more innocent Vietnamese citizens. As John Kerry testified during the Winter Soldier trials, "We found most people didn't even know the difference between communism and democracy. They only wanted to work in rice paddies without helicopters strafing them and bombs with napalm burning their villages and tearing their country apart. They wanted everything to do with the war, particularly with this foreign presence of the United States of America, to leave them alone on peace, and they practiced the art of survival by siding with whichever military force was present at a particular time, be it Vietcong, North Vietnamese, or American."

There's certainly more to be said about all of these issues, but this is likely already getting more than lengthy enough; I'd be happy to provide more information but I can't recommend the books by Rick Perlstein I've mentioned enough. Prior to reading them, my opinion about Nixon's presidency was closer to yours, but after reading through Nixonland and The Invisible Bridge, I found myself presented with a much different perspective. Conrad Black, the first Nixon biographer I read, certainly presented the entire Watergate affair as a much smaller deal, with how innocuous I felt he made it.

Sources:

Rick Perlstein, Nixonland

Rick Perlstein, The Invisible Bridge

Conrad Black, Richard M. Nixon

Chris Wallace, Kennedy and Nixon

Gary Bass, The Blood Telegram