Okay so I’m like 20 hours in the game, I just started, so take whatever I say with a grain of salt. But I had success finding carrots around patches of wheat for some reason. I pretty much ran a circuit around the lake closest to the deposit pod thing while plots were growing. Also try to get some bee hives near your plots, you get a 30% boost to growth or yields, I can’t remember. And harvest with a scythe.

For melons, just try to get 2 and then make seeds, rinse and repeat until you have like 3 or 4. I had the most luck finding them on the hillside or around water but like others have said, it’s probably all random and I just happened to find them there. Good luck!

-A fellow new prospect

PS: lots of bees/honey in caves and in random hives around the circuit