Most of the fallout will all nearby. I'd try to avoid contamination a few weeks because the radioactive Iodine has a half life of 8 days. Everything else decays too fast or too slow. (I'm not sure how difficult is to get some Iodine pills, just in case. They are quite small.)

Also, "nuclear winter" will be not as hard as the initial models estimate. I hope we don't try anyway. https://en.wikipedia.org/wiki/Nuclear_winter#Criticism_and_d...