Well, assuming whatever catastrophe caused the complete collapse of the federal government with all its continuity of government plans and contingencies, as well as the state governments – which is pretty much as near to impossible as can be without some sort of extinction level event – you’d want to seek a highly developed and free country which is capable of defending itself against any realistic external threat without American assistance (which is actually a surprisingly short list) and the strategic overwatch that has secured oceangoing trade and kept the peace over most of the world since the end of WWII. This means you’d want to seek refuge and permanent residence in an advanced nuclear state with a powerful military that can operate fully independently of the US-led alliance. That means you’d want a country with a strong navy. That narrows it down to just a couple options, but let’s continue.
You’d also want a place which has demonstrated it can survive and thrive over the long haul despite enduring some of the worst conflagrations humanity has ever seen, since a world without American power is bound to get very chaotic very fast. Given the history of the United States, you’d probably want a place which has a strong tradition as a political project rather than an ethno-state, and which has a history of permissive immigration policy since you’d be a refugee. A relatively low crime rate and well developed system of law and order, as well as good intelligence services would be a must in the post-American world. And given that the collapse of the USA would have devastating consequences for the more trade dependent countries, a relatively independent, relatively full-set economy with less dependence on far-flung trade is very much preferable to one with with a high degree of dependence on the global economy. Being a net food exporter with a robust agricultural sector is also a big green check mark.