Since the mid-1940s, spent nuclear fuel and high-level radioactive waste have accumulated throughout the country. Currently, they are stored in temporary facilities at some 125 sites in 39 states. These storage sites are located in a mixture of urban, suburban, and rural environments — most are located near large bodies of water.
In the United States today, over 161 million people reside within 75 miles of temporarily stored nuclear waste.
Current storage methods shield any harmful radiation and are presently safe. However, modern aboveground storage structures are designed for temporary storage only, and will not withstand rain, wind, and other environmental factors for the tens of thousands of years during which the waste will be hazardous.
The link also notes that the Yucca site nuclear waste will be solid, not explosive, and not flammable.
High level radioactive waste is not an insurmountable problem. While there is a significant amount of high level nuclear waste, it is also definitely finite: "If we were to take all the spent fuel produced to date in the United States and stack it side-by-side, end-to-end, the fuel assemblies would cover an area about the size of a football field to a depth of about five yards." Most small town muncipal landfills are far larger. The Lowry Landfill Superfund site, which was until 1980 a Denver landfill, is 480 acres. A football field is a little more than one acre in size.
I've previous discussed this topic at this blog in posts including: The Nuclear Waste Status Quo, Nuclear Waste in Utah, and Asking The Wrong Question About Nuclear Waste.