As the explosion of the cobalt bomb will be very powerful, probably, around 10 gigaton, it will put almost all the cobalt in the upper levels of atmosphere, may be even in space, from where it will fall all over the earth. So, there will be no localised fallout, but it will slowly falling from sky all over the world for months. For example, large volcanic eruptions were able to cover all sky for months with soot. (There will be obvious local effects too, for the first thousand km.)
Check also this link: https://www.scribd.com/doc/234366347/Doomsday-Men-Cobalt-Bomb-from-the-book-of-P-D-Smith
Note, that 510 tons is only amount of cobalt-60 which appeared in the explosion, but as cross-section is not very high, actually one needs to put many thousand tons of raw cobalt in the bomb. In the links above is said that actual weight of the bomb will be the same as battleship Missuri, that is 20 000 tons. (ITER weights 23 000 tons, typical nuclear power reactor around 1000 tons).
Cobalt bomb may include not only cobalt-60, but other isotopes like gold, strontium or polonium, for higher killing "efficiency", as they have different half-life and different biological effects.
Also, the biggest effect from the cobalt bomb will be not acute radiation (as in the novel "On the beach"), but food chains poisoning, as some isotopes tend to accumulate in food chains, like strontium.