Nothing concrete, there were attempts to build bombers that could attack the mainland USA from Europe. There was also the various U-Boat attacks and the various attempts to land spies/saboteurs in the USA.

Hitler assumed that the United States would be unable to field armies right away and that they wouldn't be able to enter the fray until 1942/1943, which in Hitler's mind was more than enough time to deal with both the USSR and Britain. Hitler foresaw some grand struggle between the New World, led by the USA, and the Old World led by Germany. It was imagined that Germany would force England into a peace treaty and than the two would ally against the common threat in America; with Britain's navy being key to attacking the Americans. Here is a quote from Hitler on the matter:

If America lends her help to England, it is with the secret thought of bringing the moment nearer when she will reap her inheritance. I shall no longer be there to see it, but I rejoice on behalf of the German people at the idea that one day we will see England and Germany marching together against America. Germany and England will know what each of them can expect of her partner, and then we shall have found the ally whom we need. They have an unexampled cheek, these English! It doesn't prevent me from admiring them. In this sphere, they still have a lot to teach us

Hitler didn't imagine a huge battle between Germany and the USA in his lifetime but rather a protracted,almost coldwar like struggle. Hitler also planned to exploit what he saw as an "Anglo-American Rivalry" and he predicted that one would eventually destroy the other. To quote Hitler again:

England and America will one day have a war with one another, which will be waged with the greatest hatred imaginable. One of the two countries will have to disappear.

Hitler also predicted that that the United States would collapse in on itself and thus a protracted struggle would be even easier to win. He imagined that once the British Empire allied itself with Germany, the American public would become angry and the American state, which Hitler had no respect for, would collapse.

In that case, what would happen to the United States? They would be territorially intact. But one day England will be obliged to make approaches to the Continent. And it will be a German-British army that will chase the Americans from Iceland. I don't see much future for the Americans. In my view, it's a decayed country. And they have their racial problem, and the problem of social inequalities. Those were what caused the downfall of Rome, and yet Rome was a solid edifice that stood for something. Moreover, the Romans were inspired by great ideas. Nothing of the sort in England to-day. As for the Americans, that kind of thing is non-existent

Finally, Hitler had next to no respect for the Americans as soldiers, which is why he was so unaffected by things like the American invasion of North Africa, because he assumed that the German military would crush the Americans. He did however, have respect for their ability to mass produce and he acknowledged their economic strength.

If we succeed this year in getting our new tanks into the line in the proportion of twelve per division, we'll crushingly outclass all our opponents' tanks. It's enough to give Rommel twenty-four of them to guarantee him the advantage. If the Americans arrive with their tanks, he'll bowl them over like rabbits

Hitler's ultimate goal was to establish German suzerainty over Europe and than lead this new German dominated Europe into the future. This was Hitler's goal, the United States wasn't the highest of priorities for Hitler.

One of the causes of the recurring mentions that Hitler had plans to invade the Americas was the "Navy Day Address" given by President Roosevelt in 1941 in which he said:

I have in my possession a secret map made in Germany by Hitler's government-by the planners of the new world order. It is a map of South America and a part of Central America, as Hitler proposes to reorganize it...

This map makes clear the Nazi design not only against South America but against the United States itself...

In the place of the churches of our civilization, there is to be set up an International Nazi Church-a church which will be served by orators sent out by the Nazi Government. In the place of the Bible, the words of Mein Kampf will be imposed and enforced as Holy Writ. And in place of the cross of Christ will be put two symbols-the swastika and the naked sword.

The part about the plots against churches has never been sourced, to my knowledge, but the 'secret map' was given to the US government by William Stephenson, a Canadian expert in political warfare working for the British Secret Intelligence Services, who claimed that it was stolen from a German motorcycle courier in South America.

According to the book "Selling War: The British Propaganda Campaign against American "Neutrality" in World War II" the account of the map was written up by three members of British Security Coordination, one of whom was the author Roald Dahl, and this was circulated after the war to select members of the intelligence services and British politicians as a top secret memento of the exploits of the spy service.

In this account the 'secret map' was not found in a motorcyle couriers bag, it was actually manufactured in Toronto by a counterfeiter at William Stephenson's behest in an attempt to draw the Americans into the war, or at least to give Roosevelt a plausible story to sell to the American public regarding why the US was entering the war.

Gerhard Weinberg touches on it in his massive tome "A World at Arms." Basically, Germany had some vague notions of attacking the US mainland eventually, but they knew they would need a large surface fleet in order to do so, which they did not have. Presumably once they had pacified Europe they would use the resources from their new territories to construct the necessary fleet (and a strategic bomber fleet, which they also lacked), but obviously they never came close to accomplishing it.

Didn't he have an architect make plans for the redesign of New York City?

Followup question, since no-one sofar has adressed possible Japanese invasion plans: in Hitler's view, wouldn't Japan be more likely to invade the U.S.? In the U.S. its view as well? Japan is closer geographically and (at first) the only one actually fighting the U.S.