Nixon was very much conservative. However the definitions change over time. The meanings today are almost the reverse of what they were a century ago. Reagan would not be considered conservative enough by today's Tea Party for example.
Nixon was also very practical. And being practical is anathema to idealogues who think that compromising is traitorous. Lowering the voting age should not have been a conservative vs liberal issue, it's just plain fair and practical to extend voting age to those we were drafting to fight and die for us. Negotiating with China may not have been the Goldwater approach, but to accuse Nixon of being pro-communist is ridiculous, the negotiation was practical and good for the country and the president's FIRST job is to govern. He created the EPA but the environment at that time was an utter shambles and the EPA was needed. Some of the most conservative people I know are very staunch environmentalists, though they'd never use that word - they hate garbage on the side of the road, they don't want pollution runoff onto their lands, the love national parks, and to use a Christian idea they want to be good stewards of the land. Back when Nixon was president, the environment was not a conversative vs liberal litmus test like it is today. Ballistic missile treaties is about wanting peace and safety, and any good liberal or conservative should want those.
Remember, Nixon helped to get the segregationist southern Democrats to switch ranks and become Republicans, which caused a strongly conservative change of direction in the party. Nixon was the ultimate authoritarian figure to the younger free speech movement and anti Vietnam war protesters, more so than any of the Democratic leadership. Nixon was for the New Federalism to give more power to local governments, an idea embraced by conservatives.
It will however be impossible to convince some people of that, especially those who think John Boehner was not conservative and secretly a democrat in disguise. Those people are a hopeless cause because they'd rather rant than think.