Funny enough, rhinos as they come have a surprisingly good sense of hearing and smell (particularly smell) precisely because they need to compensate for their poor vision. One of the reasons you may see rhinos charging at inanimate objects is precisely because they can't really see well things which are far away, and thus many choose violence. Their good sense of hearing is also important for them to be able to communicate with one another over larger distances.
However, to go from having good hearing to compensate for poor eyesight to relying 100% on echolocation can be tough. And while I didn't find anything directly saying that, the use of echolocation by shrews, oilbirds, cetaceans and bats seem to hint that for echolocation to evolve, a creature must be exposed to environmental pressures centered around having to find their way around (particularly in an obstacle-heavy habitat like caves and heavy forests) and/or hunt prey in environments where light is either scarce or nonexistent (also note that all of these creatures are either carnivores, capable of light or both, although again there's no guarantee that this correlation implies causation). Rhinos as far as I'm aware don't live in places where they encounter a lot of obstacles, nor do they need to worry about colliding with something mid-flight, and their normal food isn't something that requires much chasing. The fact that caves normally require a heavy need for the ability to climb and lower amount of nutrients (with little to no plant life, and definitely not enough to feed even a single rhino) kinda makes that hard.
The good thing however is that you don't need any special environment. Why? Because they've already been mutated by post-apocalyptic conditions.
However, since your question seems to imply you don't want to rely too much on the plot convenient effects of the classic, borderline magical Fallout radiation, let's try to come up with something that could have created the pressures we need.
I will already say that it's very unlikely it involved anything that plunged their habitat in an eternal moonless, starless night, because no light means no photosynthesis which means everything that relied on that will either go somewhere else or die unless some other producer organism is introduced to the food web and fast, otherwise no radar rhinos for us.
So, what's the next best thing to ensure our lovely rhinos can't rely on their eyes? Easy: we gouge them out. Be it because of a genetically engineered, abundant group of arthropods which began acting as the land equivalent of what denies sleeper sharks their eyesight privilege or because a new species of mutant magpies spread over the rhino's habitat and declared war over everything that had eyes, your rhinoceros often found themselves blind at an early age. The result of this would be that those with even better hearing and sense of smell, (and potentially smaller, less developed eyes as well), as well as those which were more aggressive and easily retaliate at any potential threats would likely be the most likely to survive and pass their genes, passing on their traits. So on and so forth and, with a bit of luck, it's not outlandish that we could end up with a new species of rhinos that were essentially devoid of a sense of vision and relied almost exclusively on their hearing and sense of smell to find their way around ("the rhydars are coming son, and they can smell you").
I do believe they'd keep relying on a strong sense of smell, since they are already bad at telling what the world around them is like through eyesight and their brains show strong investment in the smelling department. Their Echolocation might also be fairly rudimentary and not that effective when compared to a bat's, but it's probably not impossible. Do watch out though: the agent responsible for rendering them blind has to have a beef with rhinos specifically, otherwise it'd not be unlikely that they'd act as a strong selection factor for an entire ecosystem in which nearly all of the larger (and some of the smaller) creatures with no ways to protect their eyes efficiently would evolve into naturally blind creatures or creatures with underdeveloped eyesight, and that might even include large echolocating predators.