( I believe you can get them anywhere in it, but i mostly got them in the 'finding ingredients' scenario in Goldsea!)
I was also able to find them in the mm or through playing with companions (tho, if you want more/stacks of eggs, i think the flea market is your best bet...if there is any there)
Edit: As for the eggs nests such as
x-1
x1
Freshly Laid Eggs
Food
The seven eggs from this nest could make a rather large omelet.
Restores 10 stamina.
Designed by SevenEggs
Sells for 7
and
x-1
x1
Colorful Eggs
Food
These eggs look like candy—they're almost too pretty to eat!
Restores 10 stamina.
Designed by SevenEggs
Sells for 7
, I don't know, but i have seen them also pop up in the mole market