I'm writing a story based on people trapped in a city which has had multiple nuclear bombs set off in it, and so has some very irradiated reason. The people in it have slightly more advanced than modern day earth scientific knowledge so they know about radiation, but lack a reasonable supply chain to build more advanced technology items that function in the city like kevlar suits or computers.
They have ample materials and supplies available as would be common in a modern city that got nuked, along with a wide array of common animals around, but don't have a worldwide supply chain to source rare plants and animals from. How would they go into radioactive areas to explore?
Their supply situation is unstable, so waiting it out isn't a reasonable location, and radioactive areas often contain valuable supplies or link to key parts of the city, hence why they were nuked.
Existing questions on this matter have mostly focused on radiation being fine and not being an issue, which isn't true here due to widespead recent use of nukes, or on sourcing rare and exotic plants.
Ideal answers will help explain the sort of society and adaptions you could take to minimize the risk of going into nuked areas, and won't assume extremely rare supplies or advanced technology.