Everything you've mentioned except transportation, not counting the Interstate system, was done for national defense purposes, which are very much a duty of the Federal government.
Mercury through Apollo were political stunts. The sequence goes like this: Eisenhower let the Soviets orbit the earth first to let them establish an "Open Space" president; prior to that they were saying any satellites orbiting over their territory were illegitimate.
However at the same time we were competing for allies among the Third World, and our claims of technological superiority took a big hit. So the "space race" began. First was of course Mercury, put a man in orbit, then a couple of years later JFK committed us to "landing a man on the Moon and returning him safely to the Earth"
But it was just a stunt, leaving no infrastructure in place, heck, even finished Saturn Vs were left outside to rot (due to the inevitable delays, Nixon had to cancel the last planned Moon missions because of the sunspot cycle making them too dangerous).
The Interstate system was based on the German Autobahns, and President Eisenhower's experience trying to move on troops on our old system. However we've had a long and very mixed history of Federal involvement in transportation systems, such as the transcontinental railroad scams (see e.g. http://en.wikipedia.org/wiki/Cr%C3%A9dit_Mobilier_of_America... or which went bankrupt (hint: the land grants were the real prize)).
The Internet was developed by/for/with the Defense Advanced Research Projects Agency (DARPA) to allow the sharing of the then very expensive computers.
I trust we all know what pushed the initial development of atomic energy in the US, and as I understand it our first reactors developed to specifically produce power were for submarines, where they made a massive qualitative difference.