I can't say how many days before it would be 'safe' for you to go outside. Being able to measure how hot it is outside your place is critical.Supervisor42 can explain it better than I, but from what I have read and understand the most harmful isotpoe that comes out of a nuclear explosion is Iodine 131. All of the Iodines are attracted to the thyroid. Iodine 131 has a half-life of 8 days ergo after 8 days half of the I-131 will have decayed away. After another 8 days half of what is left will decay away, and that will continue until it is finally all gone.
Think of a half life like evaporation only on a very percise and measurable level. If you left a glass of water standing out after a period of time it would no longer be full. It will evaporate away. Half life works the same way, but it is a specific rate of decay for every isotope.
There are isotopes that come from a nuclear explosion that will last for years, but they are not nearly as high or as dangerous.
If you got little-none, one day; if you got a bunch, 2 weeks may be barely enough.
As far as the I-131, the thyroid, and the use of KI, I have to avoid the soapbox and just say, read up on how it offers no benefit for people over 50.
The soapbox = they have convinced so many people that all they need to do is to take the magic-pills that they sell, and they will be completely safe from radiation.
Again, knowing how 'hot' it is at your place is the most important part. Prepare.