If there is a nuclear leak or a bomb is dropped, you're probably going to know about it. If a bomb is dropped, you need to take shelter ASAP, change your clothing and wash off any possible radioactive dust. If the S has HTF, what good will it do you to know your radiation level?
If you shelter in place, some kind of radiation detector could help you decide when to leave.
Obviously if you are too close to ground zero you won't survive at all, but there is also likely to be fallout that affects a much wider area than the initial explosion. The really nasty stuff fortunately has relatively short half-lifes so it should be viable to wait it out. Also, it takes time to fall so you could have an opportunity to get to your shelter before the outdoor environment becomes too hostile. I gather we're talking about remaining indoors for a couple of weeks, preferably within some kind of improvised radiation-shelter that you can discover how to build on the internet, within your house (which you also should seal against dust).
"Running away" would also be a viable plan, but I'd rather shelter in place if I can. With fallout you are at the mercy of the winds and anywhere that you might run to could be affected if the winds shift. I'd rather be indoors with my gear. Being self-sufficient for a couple of weeks is also a good goal for a number of other disaster scenarios.
You could rely on news reports to tell you when the fallout has decayed to safe levels, but there could be local variations so having your own measuring device could enable you to leave earlier than otherwise if the news reports are conservative, or it could warn you if the news reports are optimistic. And of course it's nice to be self-sufficient.