How to store hard boiled eggs
Best place: the fridge. USDA gives hard boiled eggs a fridge time (1 week, from purchase) and no pantry time, so they belong in the fridge as soon as you get home.

Where these times come from. USDA FoodKeeper has no entry named "hard boiled eggs". The times on this page are the USDA figures for hard boiled eggs, copied without change from its Eggs entry. The full entry lists other kinds too.
No guideline
1 week
from purchase
Not recommended
How to tell hard boiled eggs have gone bad
- A spoiled egg gives off an unpleasant odour as soon as you break the shell, raw or cooked. Crack each egg into a separate bowl so one bad egg does not spoil the rest.
- An egg that floats in water has a large air cell. USDA says that makes it old and of poor quality, not necessarily unsafe: crack it and check for an off odour or an unusual look before deciding.
- Cracked or leaking shells let bacteria in. Do not buy cracked eggs; if one cracks on the way home, break it into a clean container, keep it refrigerated and use it within 2 days.
- A grey-green ring around the yolk of a hard boiled egg comes from overcooking. It is harmless and not a sign of spoilage.
- Eggs in the shell keep 3 to 5 weeks in the fridge from the pack date; hard boiled eggs about 1 week. Past those windows, use the odour test and throw out anything doubtful.
Sources: Shell Eggs from Farm to Table (USDA FSIS). The times on this page are quality guidelines, not safety limits; food that shows these signs goes out regardless of the date.
Storage habits that make the difference
Keep dairy and eggs in the coldest part of the fridge, not the door, at 40 F (4 C) or below. Store eggs in their original carton to protect them and track the date. Reseal cheese tightly in wax paper or a container, and keep milk capped between pours.
How to store other dairy products & eggs
Source: USDA FSIS FoodKeeper dataset (public domain). How we decode the data.