My fear for the delivery of an actual terrorist nuclear device would be in a standard shipping container aboard a cargo vessel, perhaps combined with a takeover of the cargo vessel itself in order to force it in as close as possible to, e.g., the civilian population ashore, a large cruise ship with many thousands aboard, or vulnerable fuel or chemical tanks, etc. It is extremely hard to stop a large cargo vessel and neither the military nor the USCG are likely to have the means immediately at hand to do so.

A far simpler but probably far more likely "dirty bomb"used to spread radioactive debris with a conventional explosion could be easily employed as you suggest, and many other means, as well.

Basic radiation detectors are becoming more affordable, easier to use, and more widespread. They are increasingly common in places like ERs and on fire apparatus. One time use detectors are very cheap, a simple continuous keychain-sized radiation detector like the "NukAlert" is available for under 150 bucks, and more sensitive sophisticated monitors are under 1,000 dollars.