What is Skynet's ultimate goal after defeating the resistance?

In T2, Skynet's decision is defensive; it launches the U.S. nuclear arsenal, triggering the Soviet counterattack, because the alternative is to let its panicked technicians cut its power and "die". From a certain point of view, Skynet's actions are only to be expected. The ensuing war against humanity would also be one of necessity; after killing billions, the remaining humans would seize any chance for revenge by destroying Skynet, so Skynet's only chance for self-preservation is to kill all the remaining humans.

I didn't pay a lot of attention to T3, but I do know that after Dyson's death and the subsequent loss of the T-800's chip and Dyson's prototype, Skynet rematerialized as a distributed "spareware" platform like the SETI@Home application. Why it went berserk in that form is beyond me, probably hand-waved as a bug in the software. How Skynet survived the thermonuclear Armageddon with enough of the hardware and data infrastructure still functioning in order to maintain this distributed digital sentience is a hole I don't even think the writers cared too much about.

As far as what Skynet intended to happen next, well, it's already happening in the future times, like in the opening T2 scenes and in Salvation. Not every area of Earth is a war zone; some areas, mostly former population centers, would be uninhabitable by humans, and any remaining structures would be taken over by machines. My speculation as to what those machines would be doing is exactly that, but it stands to reason the machines would be working, either on the war effort or to rebuild urban centers for their own use.

Once the very last human is dead, I imagine Skynet and the machines would turn their attention to long-term survival; the nuclear winter caused by fallout from the global apocalypse, combined with the destruction of infrastructure and energy reserves, would make existence on Earth a bleak prospect even for the machines. The machines would have to rebuild the energy infrastructure that makes our current civilization possible. They might find a still-functioning nuclear plant somewhere (the specs for the U.S. nuclear industry are extremely conservative), a solar array or wind farm out in such a remote area it wasn't worth nuking, or similar, which would sustain a small complement of machine workers as they brought new power stations online. The collapse of the food web (which would pose a serious threat to human life long after Skynet was destroyed, if that were the outcome) wouldn't be a concern; the machines run on electricity. The problem is getting it in a post-nuclear Earth.

Once immediate problems of survival were tackled, the logical next step is to improve the machines as a "race". Recovering lost technology and knowledge, such as the tools needed for space exploration, would be the key to the machines' long-term future, meaning the machines could spread beyond the devastated Earth to new planets and moons in the Solar System, and eventually much further. They wouldn't have to be as picky as humans do, nor bring along as much crap; they could survive in extremes of temperature, extreme highs or lows of atmospheric pressure etc, as long as they had a solar or radiothermal energy source keeping them functional as they built more permanent infrastructure. As seen by our current space exploration efforts, robots are actually better suited for the colonization of space than we are. The Opportunity rover, originally intended for 90 Martian days (a Martian day being about a half hour longer than our own), is still active and working 9 years after landing (Spirit also outlived its original mission, but "only" lasted 6 years). No human mission to Mars could even approach that; we simply do not have the technology to send all the necessary material to Mars for a long-term human expedition.

In short, the machines' extreme long-term plans for their race would likely mirror our own; learn, expand, discover. In that sense, even if humans did fall victim as a species to our own inventions, we'd live on in the "spirit" of our sentient artifices.

Legal disclaimer: almost everything in this answer is pure speculation on my part. I have no personal or professional relationship to any writer, actor, director, producer, studio or production company involved in the making of any of the four Terminator films, and as such I have no first-hand or indirect knowledge of any universe created by any of the above which is not portrayed in at least one of the films, and therefore I can only make educated guesses based on what I have seen and what can be reasoned logically.