The reality is that isotopes with short half lives (measured in weeks, or days) are dangerous as hell. They emit gamma radiation at prodigious rates and that's what gives you radiation sickness.
The slow half life isotopes primarily emit Alpha, and Beta particles. Both of which are stopped by a sheet of paper. So long as you don't ingest those isotopes, you will be fine. Even if you did ingest them, you will most likely die of heavy metal poisoning long before the radiation kills you.
I have traveled through Chernobyl twice. Once 5 years after the accident, and again after 20 years. Both times I was with a guide, and we each had Geiger counters.
The first time there was significant radiation on both sides of pretty much all of the roads. There was just so much material that had collected in the low lying areas that even though the half lives were relatively short, there was just a ton of material to process.
After 20 years the vast majority was clear. There are still a couple of small pockets that are still "hot", but because the isotopes are of the slow decay variety, so long as you take simple precautions, you are safe.
That's why I say, you wait a month. After a month the rapidly decaying elements have devolved into their daughter elements and expended their gamma radiation. At that point, simple precautions allow safe travel in most places.
