Somewhat realistic. Use a Cobalt Bomb.
For a realistic dirty bomb that has a has a 50 year minimum, city-sized lethality, where "realistic" is assumed to be a combination of cost-effectiveness and technological/military feasibility rather than political tenability, you'd want a Cobalt Bomb.
As defined by Wikipedia: a cobalt bomb is
a type of "salted bomb": a nuclear weapon designed to produce enhanced amounts of radioactive fallout, intended to contaminate a large area with radioactive material.
Basically a nuke wrapped with a layer of cobalt. Simple but extremely effective at area-denial because:
Areas irradiated by fallout from even a large-yield thermonuclear weapon begin to increasingly become habitable again after one to six months; a cobalt bomb's fallout on the other hand would render affected areas effectively stuck in this interim state for decades of habitable, but not safely so under constant habitation, conditions.
By not safe, this means:
After 10 half-lives (about 53 years), the dose rate would have decayed to around 10 mSv/hour. At this point, a healthy person could spend 1 to 4 days exposed to the fallout with no immediate effects.
At its worst, it has been theorized that one device
containing 510 tons of Co-60 can spread 1 g of the material to each square km of the Earth's surface (510,000,000 km2). Radiation output from 1 g of Co-60 over one half life is equivalent to 44,000 GBq, which is sufficient to kill any inhabitants. If one assumes that all of the material is converted to Co-60 at 100 percent efficiency and if it is spread evenly across the Earth's surface, it is possible for a single bomb to kill every person on Earth.
In practice, the efficiency is much lower but (using back-of-the-napkin math) we can estimate that dispersal of 100kg of cobalt at an abysmal 1% conversion will have a lethal effect over 1000km2, 100 times the minimum. Considering that New York City is only 789km2, this amount is sufficient to convert most metropolitan cities into necropolises for the next few decades.
Prior to being relieved of his duties, Douglas MacArthur promoted the idea of using Cobalt across the Korean Peninsula. As he recounted in his memoirs:
Of all the campaigns of my life, 20 major ones to be exact, [Korea was] the one I felt most sure of was the one I was deprived of waging. I could have won the war in Korea in a maximum of 10 days.... I would have dropped between 30 and 50 atomic bombs on his air bases and other depots strung across the neck of Manchuria.... It was my plan as our amphibious forces moved south to spread behind us—from the Sea of Japan to the Yellow Sea—a belt of radioactive cobalt. It could have been spread from wagons, carts, trucks and planes.... For at least 60 years there could have been no land invasion of Korea from the north. The enemy could not have marched across that radiated belt."
Note that, he's arguing not for detonating but dispersing, which is directly in line with area-denial and not necessarily with immediate mass-murder.
As for actual implementation: the U.S. investigated the idea in the 60's but chose not to move forward, for reasons not formally stated. The British gave it a go and after some setbacks, withdrew (thus the "somewhat" qualifier). Russia, on the other hand, does not have the same qualms and is rumored to have a few warheads stockpiled.
For further reading, I recommend:
Specifically, the "Real Life" section.