The most 'realistic' threat for your survivors to face is simply environmental factors - lack of access to safe water or enough food, and competition for resources against other more desperate and less morally upstanding people.
But from your suggestions, I'm thinking you want something more exciting. Depending on the history of your nuclear war, a good solution might be
The enemy that the nuclear weapons were used against
Regular people didn't get a lot of warning when the bombs fell, and they certainly didn't get a detailed understanding of why they fell. Your American survivors assume that Russia or China launched first and the US responded. Russian and Chinese survivors assume it was the Americans that went crazy. Nobody knows for sure, because any way of finding out was destroyed along with the rest of humanity.
It was one of those countries, and knowing they were about to start an apocalypse they put certain measures in place to protect their citizens and military - and now they're coming to claim the desolate landscape.
It was a threat nobody had considered - a supervillain or evil group that collected enough weapons, or at least influence over the people that own those weapons, to cause the disaster. Now the next step of their plan can begin.
Or maybe the threat was something else entirely:
A few days before zero-day, something appeared on deep-space monitoring scans. By the time the information reached the top levels of government, that something was already here, and spreading everywhere. Decisions were made, and countries fired on their own cities to defeat the threat. Your survivors never saw the something, but it/they survived, and it/they is still out there.
A horrifying disease that turns people into horrible monsters began spreading across the world. Selfish leaders decided that the best way to protect themselves was to retreat to their bunkers and destroy everything else. Your survivors were in an isolated location and didn't experience the spread, but the bombs didn't kill all of the monsters - and they're hungry. There's also locations scattered across the world filled with the rich and powerful and their staff/servants/slaves, who may yet play a part in the future of the world.
Or if you really want what you mentioned:
A series of portals to another dimension began opening across the earth, and monsters began pouring out - trihorns, giant scorpions, skinless to name a few. The governments of the world all reacted at almost the exact same time and launched their nuclear weapons against the threat, devastating the earth. While this was successful in closing the portals, the creatures remain.