*snip* should you be able to remove the fallout at all, or should the tile be a permanent wasteland? Can this be done in real life?
On a small scale, certainly, radioactive cleanup can be done. Look at Fukushima, for example.
And not all radioactivity is instantly lethal, at least over the short term: alpha and beta radiation can actually be blocked by ordinary clothing (although that's not recommended as protective gear!). Admittedly, you really don't want to ingest alpha-emitters (that's what killed that Russian guy who was poisoned by polonium in London a couple of years back), but so long as you can avoid inhaling radioisotope-laden air, drinking radioisotope-laden water or eating food grown in radioisotope-contaminated soil, you should be OK in that regard.
Gamma radiation is a problem though: you need at least a couple of feet of concrete and lead to block it. Since fallout usually contains emitters of all 3 types of radiation, and the type of radiation changes as the radioisotopes decay into lower-mass and more 'stable' elements (i.e. ones with longer half-lives), cleanup basically involves washing down and/or collecting up radioisotope-contaminated material (including building-materials and topsoil if necessary) and disposing of it in such a way that the remaining radioactivity is contained (e.g. by burial in old mineworkings) until emissions drop to safe (i.e. 'background') levels.
On a large-scale, I think you answered your own question, as to the practicality of cleanup-ops...
I understood the land around Chernobyl was uninhabitable...
Well, it's 'only' been 30 years since that accident, and successive Russian governments since then had other priorities, what with the USSR collapsing, insurrections in the former Soviet states, and all.
Although people now live in Hiroshima and Nagasaki right?
Yes they do -- both cities have been completely rebuilt. Hiroshima's population had actually returned to pre-1945 levels by 1955, and 70 years later, residual radioactivity has returned to 'near-background' levels.
In 1945, cleanup was possibly not a high priority there, either (remember, this is an era when doctors were paid to advertise smoking as a healthy habit!) -- and what was done may not have been as effective as the techniques used today. But the casualty count from radiation sickness at the time might also have been (much) lower, had the US Govt of the time not made the decision to treat the bombsites as field-research sites for a classified military medical experiment, and withold the (classified) data collected from people to whom it might have been useful, such as Japanese doctors.
(Acute radiation sickness was already known about, due to accidents during the Manhattan Project, amongst others, but not so much was known about the long-term effects of lower-level exposure).
That said, the bombs dropped on Japan were relatively low-tech, inefficient devices that spread a lot of isotopes around. Modern nukes use much less radioactive material per warhead than FatMan and LittleBoy, and generate much greater explosive yields, primarily as a result of increased efficiency of fissioning, and hence produce far less radioactive fallout per megaton (because more of the isotopes have been 'burned' during the detonation).
Of course, the idea that a nuked civ would actually be able to muster the organization and manpower required for fallout-cleanup immediately after a global nuclear war is fairly moot...