Pakistan nuking India is the most likely, for obvious reasons.
Though likely, you have to consider that Pakistan endangers itself to radiation by nuking India.
Pakistan couldn't nuke America, because It'd be shot down well before it ever made it to the continent.
You can't prove that. Pakistan might be much poorer and underdeveloped than America, but if we're talking about full fledged war, you can bet yourself that if Pakistan wanted, they could launch all nukes at once and load some on as cargo.
Also, Pakistan having middle eastern allies, the missiles could come from any middle east controlled area in the world.
I'm not stating that it's 100% likely Pakistan can nuke us, but I think it's outrageous to assume the Atlantic Ocean is going to still be our first line of defense and awareness in the 21st century.
And land, because with an actual war against a country, we can use pretty much whatever seems fit. We won't to worry because if anyone acts suspicious, we can just shoot them.
Nope, it won't work like that.
First, we'd need reason to go to war. Secondly, we'd need to blame someone. Our goal can not be to eradicate an entire country. I'm not sure even the American people, let alone the international community would stand for it.
Also, I'm not sure our infantry would do the sweetest job like you say. Karachi alone is a city with 7-9 million people. I'm not sure how easy it would be just to shoot anyone that messes with you.
You forget that India and Pakistan are arch-enemies on the Middle East playground. If we lose Afghanistan as a staging point, we'd just gain India.
South Asia, not Middle East. [Not trying to be rude, just removing stereotypes if they exist].
Also, I doubt we would just merrily gain India. Though India and the USA are good friends, it would be stupid for the US to try to use India.
India might just reject the offer because they're a pretty strong military force that might not want the USA using their land as a staging point for attacks [and, if the worst comes, an area for attack].
Furthermore, if India does join in, this war becomes much more global and I can definitely see China and Russia picking sides, with China giving more support to Pakistan I would assume.
Lastly, the India/Pakistan border is so heavily guarded that America, even with all of its military might and equipment, would suffer excessive casualties charging through it. We barely know the turf, let alone the fact that huge portions of the barrier are either nasty desert, walled, or defended.
Also, Pakistan would be much more for the war than America [Self Defense > Attacking Pakistan from America, of course]. So American support for the war would deteriorate quickly, and there is no way you can deny that American troops would die.
Finally, just a history reminder. Pakistan has successfully defended itself from India in the past. Every time. Even at times when it was 'close to the brink', Pakistan, a nation much poorer and less populated has held off due to these factors such as military control, population density, and serious national pride [No joke].
I'm not saying America would lose, I'm sure if we tried hard enough it would be a somewhat Vietnam scenario where we either pull out or we ravage the entire country or both.
I'm also extremely sure that it wouldn't be a simple walk in the park.