One troublesome relic of the Cold War for Russia is the thousands of bomb shelters built when communists bureaucrats ran the Soviet Union. Nuclear weapons frightened the communist officials, and they planned to actually participate in a nuclear war, and survive. Thus, from the 1960s, they began building more shelters, eventually enough to hold five percent of the population (nearly 15 million people.) Because of the size of the Soviet Union, much of the population were expected to survive simply because they were far from where the A-bombs were going off. The shelters were mostly for the communist party members and government officials living in metropolitan areas deemed likely targets for enemy nukes.
Through the 1990s, the lack of money to maintain these shelters, led to most of them being abandoned. Some, especially the more elaborate ones for the senior leadership, were kept up, and remain ready. But most of them are seeking a use, because there's no money to dismantle them either. Without that, these structures will last a long time. In the West, thousands of concrete fortifications remain from World War II, especially in the countryside where there was no new construction that warranted demolition. Many have found commercial use; for storage, growing mushrooms or even as factories. In some poor nations, the underground facilities became homes. Many of the aboveground fortifications become tourist attractions, and are more likely to acquire second lives as homes, or, in remote areas, shelter for hikers or hunters.
A major problem with these underground shelters is water. Many are built beneath the water table and are not waterproofed sufficiently to keep water out. Unless pumps are kept going all the time, they flood. Leaving the water there for a decade or more weakens the structure and makes them unstable, and dangerous for anyone poking around. Even with that, concrete lasts a long time. The Romans developed a very modern version of concrete, and many of their structures built with it survive some two thousand years later. So we can expect these Cold War relics to outlast most other artifacts of this period in history.